The electric potential at the center of a hemisphere of radius r and having surface charge density s can be found by using the equation V=k*s/r, where k is the Coulombs constant. The potential difference (V) between two points in an electric field is: The work done in bringing a charge of +1 C from one point to the other (potential energy per coulomb) Unit: joule per coulomb ( J/C) or the volt (V) In other words, it is the energy of a thin spherical shell of charge Q, with the same energy of a uniformly charged sphere. An electric field is defined as the density of the charged gas () and an electric field is defined as the density of the charged gas (). Potential difference between any two points In the electric field is defined as the amount of work done in moving a unit positive charge without acceleration from one point to another along any path between the two points. W AB = -V AB q. It only takes a minute to sign up. Step 1: Determine the strength of the field and the distance between the two points. The electric charge of matter controls the interaction of elementary particles in an electric or magnetic field. Earth is typically used as a reference point, but any point beyond the electric field charge can be used as well. Connect and share knowledge within a single location that is structured and easy to search. A voltage which is a measure of electric potential difference, is the cause of electrical current to flow in a closed circuit. The formula of potential difference between the two points is: Work done q = K e Q (1 r1 1r2) Furthermore, the potential difference (voltage) can be calculated by Ohm's Law with the help of the . If it had moved the charge from a distance of $r$ to $r+dr$, where $dr$ is a very tiny distance, the work $(dW)$ would have been approximately equal to $K_e\dfrac{Qq}{r^2}dr$, where $K_e$ is Coulomb's Constant. The sum of all these little 'works' will be the total work done by the external agent when it moves $q$ from $B$ to $A$, which will be : But I say it's ##-20 V## as electric field is conservative and I can find potential difference as work done in moving a unit charge from ##A## to ##D## then to ##C##. If we assume the north pole is in the positive z-direction, then more work is required to approch from infinity to the minus z-direction. The more potential an area has, the more energy it requires to generate. There is no intersection between the field lines. 1 Crore+ students have signed up on EduRev. The given problem is based on the work done to shift a charge from one point to another.. Why do we use a calculus based approach for calculating the work done when a charge moves a certain distance in a system of two charges? But I say it's as electric field is conservative and I can find potential difference as work done in moving a unit charge from to then to . Electric field lines can show the properties of electric fields based on their nature. Potential difference between ##D##and ##A## should be a big zero as we are moving perpendicular to the field and potential difference between ##C## and ##D## is ##-20V## so the overall potential difference between ##C## and ##A## should be ##-20V## and not ##-10\sqrt{2}##. Between two points A and B we may write. An electrons total energy in an electric field is defined as the sum of its kinetic energy and potential energy. The proportionality constant is the permittivity of the medium. Hence, the correct answer is option A. The electric field can be used to find the potential difference between two points in space. I have been told to calculate the potential difference ##VC - VA##. capacitor. $$\dfrac{\text{Work done}}{q} = K_eQ \Bigg ( \dfrac{1}{r_1} - \dfrac{1}{r_2} \Bigg )$$ There is no vector addition involved. It usually has a high resistance so that it takes negligible current from the circuit. It's not different (as long as the currents/fields are not changing very fast). The electric field can be found by using a Gaussian surface. Consider two points A and B separated by a small distance dx in an electric field. pharmacy near me 5MP 1920P PoE Night Vision Security Surveillance System Camera from $549.95 Select options 5MP HD POE Two Way Audio CCTV System from $599.95 Select options 5MP PTZ Speed Dome IP 20 X Zoom Lens 60M IR Night . Note 1 electron volt = Charge on one electron x 1 volt. The distance between two points is the shortest distance between them. There are specific properties, rules, and applications to electric field lines. When a positive test charge is transferred from one location to another, there is increased potential energy and electric potential. Your equations and reasoning are correct. An electric potential hemisphere is a half-sphere of electric potential. The potential difference between two points is equal to the electric field times the distance between the two points. [Note : If this is wrong, please correct it, I'm just a beginner to calculus] The SI unit for voltage is the volt. So I have been given a uniform electric field ##\vec{E}=20 V/m## in the direction as show in the image. Thorstein Veblen. Is The Earths Magnetic Field Static Or Dynamic? The electric field is equal to the resistivity of the material multiplied by the current density. This means that at the same point in time, the electric field and the magnetic field are inversely related. We are heading from A to B with a potential of 56.6 volts at the first energy level, which means we have a positive main charge and its electric field lines point in an inward direction. On equipotential surfaces, concentric shells will be used. The electric field can be used to find the potential difference between two points in space. The free movement of a positive charge in an electric field will move it from its highest potential point to its lowest potential point. A little question though, how is potential difference in an electric field due to a point charge difference from potential difference in a circuit? To learn more, see our tips on writing great answers. volt. The potential of a hemisphere in the center with constant surface charge density is given by its radius, R2, which is equal to its surface charge density. Let's say that the external agent moves $q$ from $B$ to $A$. Assume the great circle of the hemisphere sits on the xy plane and the nort pole is in the positive z-direction. When the electron moves, it must overcome the electric field in order to achieve potential energy. Depending on how the system behaves, potential energy may increase or decrease with distance. Is The Earths Magnetic Field Static Or Dynamic? The Attempt at a Solution. If the charged object is a sphere, the build-up of charge will produce an electric field that extends from the surface of the sphere in all directions. Is an electric field inside a solid? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Work done = charge x potential difference. Electric potential is affected by a number of factors, including the type of charge, its amount, and its location in the electric field. To put this equation into practice, let's say we have a potential . The equation is as follows. Why is the electric potential at a distance of $R$ from a point charge $q$ equal to $\frac{-q}{4\pi\varepsilon_0 R}$, Electrostatic Potential Difference Between Points, Textbook question on calculation of potential difference between two points. by Ivory | Sep 16, 2022 | Electromagnetism | 0 comments. If i have an uniformally charged hemisphere with its center at the origin, how do i calculate the electrostatic potential (or field) at each point? When a charge moves through the electric field work is done which is given by. Electric potential is defined at a point. When a charge is moved between the two points, then some work is to be done, which gets stored in the form of . The potential energy decreases with repulsive forces, and increases with attractive forces. To find the potential difference, we need distance. If the charged object is moved away from the conductor, the build-up of charge decreases and the electric field diminishes. Potential difference is defined between two points in electric field. The potential difference between two points is the work done per unit charge in moving a charge between those points. The potential at the top of the hemisphere is higher than the potential at the bottom of the hemisphere. Field lines parallel to the surface of the charge are formed. The electric field at a point is perpendicular to the Gaussian surface at that point. A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. The potential difference will be positive if the electric field is pointing from the first point to the second point. Moving farther from a charge distribution reduces the electric potential energy of a charge. Why is there no other disc in the Universe? This physics video tutorial explains how to calculate the potential difference between two points in an electric field on a metallic conductor. This physics video tutorial explains how to calculate the potential difference between two points in an electric field on a metallic conductor. In an electric field, the potential difference between two points is proportional to the magnitude of the electric field. The dimensions of electric field strength can be calculated in relation to the length. Electric fields are well understood to be characterized by their magnitude based on their density. The force is therefore considered attractive because the work it does is negative, regardless of how negative it is. How Solenoids Work: Generating Motion With Magnetic Fields. The Higgs Field: The Force Behind The Standard Model, Why Has The Magnetic Field Changed Over Time. The force acting on a unit positive charge at A is equal to E. Now, the work done in moving a unit positive charge from A to B against the electric field is dW=Edx. The electric potential at the edge of the hemisphere is equal to the potential difference between the two conductors. A charge is applied to move an electric field, and electric potential is an estimate of how much energy it requires to move it. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Their problem is that the length of the diagonal is not 1 m, it is ##\sqrt 2## m. 2022 Physics Forums, All Rights Reserved, Problem with two pulleys and three masses, Newton's Laws of motion -- Bicyclist pedaling up a slope, A cylinder with cross-section area A floats with its long axis vertical, Hydrostatic pressure at a point inside a water tank that is accelerating, Forces on a rope when catching a free falling weight. Why do American universities have so many general education courses? Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. A non-uniform electric field is one that does not appear to have uniform properties. NCERT English Solutions, Science Solutions, Social Science Solutions, and Business Studies Solutions are all covered in the NCERT Newsquiz each week. Electric potential between 2 charged spheres -- problems with sign? The electric potential of an electron is a measurement of the energy it can produce. The distance of $Q$ from $A$ is $r_1$ and from $Q$ to $B$ is $r_2$. \begin {tabular} {c|c} V = qW ond & P = T E \\ V =Ed & P = RV 2 \\ C = V q & \end {tabular} Previous question Next question. Is it different at all? One way is to follow the definition of electric potential difference between two points and . The SI unit for electric field is the volt per meter (V/m). Force is applied opposite to q o E to . So, it would be equal to : The field near a system of charges can also be described by a scalar quantity known as the "Electric Potential". The electric potential at the center of the hemisphere is zero. Now, this is the work done by the external agent when it moves $q$ from $B$ to $A$. dE = 1/(4piepsilon_(0)) (dq. Is this formula I derived for Potential Difference between two points in an electric field correct? For obtaining the potential difference between the points A and C, we algebraically add the potential differences ${V_{AB}}$ and ${V_{BC}}$. This is the most common type of electric field, as you can see. If the distance between the two objects grows larger, there will be more and more potential energy required. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. in volt (V) W = work done in driving the charge between the two points in joule (J) It also explains how to calculate the current density given the electric current and the diameter of the material. This is how the electric flux is obtained on a surface S by using *br. Is it correct to say "The glue on the back of the sticker is dying down so I can not stick the sticker to the wall"? How is the merkle root verified if the mempools may be different? Electric potential is the work done per unit charge to bring the charge from infinity to a point in an electric field. The energy required to move the given charge from point A to point B is of .. Sect.3 states that the electric field immediately above the surface of a conductor is perpendicular to the surface of that conductor. This is known as an electric field hemisphere. Sudo update-grub does not work (single boot Ubuntu 22.04). How does the potential difference between two points in an electric field be the work done? The potential difference between two points in an electric field is defined to be the work done to move a unit charge from one point to the other. The potential difference between two points in an electric field is defined as the work done or the energy that would be required to move one coulomb of charge from one point to another. Thanks for contributing an answer to Physics Stack Exchange! In the nineteenth century, Michael Faraday proposed the concept of electric field lines. Appealing a verdict due to the lawyers being incompetent and or failing to follow instructions? According to the teacher (on YouTube) the potential difference . The potential difference will be negative if the electric field is pointing from the second point to the first point. An electric field is an electric field that is uniform throughout a region. A string stretching for 20 cm can store approximately 50 watts of energy. the energy required to move a charge of 8.00x10^-19 coulomb from point a to point b is 1 See answer Solution. The units of electricity in an electric field are volts per meter. In symbols: Where, V = potential difference (p.d.) If a unit charge can be moved from one point to another against an electric field, it has an electric potential. There are no clear patterns in the field at every turn. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. When would I give a checkpoint to my D&D party that they can return to if they die? An electrons potential energy in an electric field is expressed in equation U(r)=-qeV(r). In conductive materials (resistors), current flows from high potential to low potential, since E-field (and hence the force on positive charges) points from high potential to low potential. The direction of the electric current and perpendicular to the electric potential field are always the same. Transcribed image text: The potential difference between two points in a uniform electric field is 500 V. The distance between the two points is 2.5 cm. It is never a coincidence that electric field lines are always straight and parallel to one another. Help us identify new roles for community members. a device with a specific capacitance that is used in electric circuits to store electrical energy. And by distance, I think the distance should be from the electric charge to the point, but there is none. 1 j/c. Let's assume that we have a positive charge $Q$ and a positive test charge $q$ is moved by an external agent from a point $A$ to $B$. the potential difference between two points, a and b, in an electric field is 2.00 volts. This video contains plenty of examples and practice problems.New Physics Video Playlist:https://www.youtube.com/playlist?list=PL0o_zxa4K1BU6wPPLDsoTj1_wEf0LSNeRAccess to Premium Videos:https://www.patreon.com/MathScienceTutorhttps://www.facebook.com/MathScienceTutoring/ Is there a disc which goes through the origin and intersects the hemisphere? A Gaussian surface is a closed surface that encloses a charge. Newtons per coulomb: this is the equivalent of volts per metre for these new units. The potential difference between two points is said to be 1 volt if the work is done in moving 1-coulomb charge from one point to other is 1 joule. Sed based on 2 words, then replace whole line with variable. An electric potential difference, also known as a voltage, is the difference in potential between two points. Asking for help, clarification, or responding to other answers. Use MathJax to format equations. What are the properties of electric field line? Potential difference between two points in an electric field is defined as the amount of work done when a unit positive test charge is moved from one point to another. The electric potential, also known as the voltage, is the difference in electric potential energy between two points. I think that that should give the potential difference between two points in an electric field due to a charge $Q$. A charges potential energy is determined by how much potential energy it has. W AB =F.d=q o E.d=q o Edcos =q o Edcos180=q o Ed(-1) = -q o Ed. This results in a build-up of charge on the surface of the conductor. Given data: The potential difference between the points A and B is, V' = 2.00 V.. A spherical Gaussian surface will not contain more than Qs total charge than a sphere of uniform charge because electric fields inside a sphere are radially outward (by symmetry). What is the electric field intensity? Step 2: Use the formula {eq}\Delta V=Ed {/eq} to calculate the potential difference between the two points . In a superposable field, the electric field is extremely active. by Ivory | Sep 19, 2022 | Electromagnetism | 0 comments. V A-V B =W AB /q o. Keep in mind that whenever a voltage is quoted, it is understood to be the potential difference between two points. We can observe the electric field in any function because of this differentiation process. How to connect 2 VMware instance running on same Linux host machine via emulated ethernet cable (accessible via mac address)? According to the teacher (on YouTube) the potential difference ##VC - VA = -10\sqrt{2}V##. The potential difference between points A and B is given by. Let's consider a simple circuit which consists of a power supply, an electromagnetic force, let's say a battery, such that the potential difference between its terminals is equal to 10 volts. The electric potential difference is the difference in electric potential between two points in space. The electric field of X and Y will be the same. Its as simple as that to judge the field at any given point. What is the electric potential between two points? the ratio of the net charge on one plate to the potential difference, measured in farads, between two plates of a capacitor. Voltage is the work to be done, upon an unit charge to move between two points, against a static electric field. When a block is released, it generates a kinetic energy that can be converted into potential energy. Should I give a brutally honest feedback on course evaluations? " A potential difference of one volt exists between two points when one Joule of work is required to move one Coulomb of charge from one point to the other". So, my desperate move is: V = E.d = 6000 x 0.5 = 3000 V , where 0.5 is the distance between X and Y? It is connected in parallel. It may not display this or other websites correctly. How to set a newcommand to be incompressible by justification? The electric field between two electrodes is straight because the electric potential difference between them is constant. The electric potential decreases in the direction of the electric field lines in this manner. When a charged object is brought near an uncharged conductor, electrons in the conductor are attracted to the charged object. The potential difference between two points is equal to the electric field times the distance between the two points. When there is a relative closeness of the lines at that point, the intensity of the electric field is calculated. The potential difference is the work done per unit charge as it moves from one point to another. The first step in determining the electrical potential is to find a point of *x0 with V(*x0)=0 in an electric field. Can virent/viret mean "green" in an adjectival sense? It does some work while doing so. Thus, the potential difference between two points is directly proportional to the electric field and inversely proportional to the distance between the points. To find the potential difference . It is the relation between electric intensity and potential difference. An electric field line is a imaginary line or curve that is drawn through empty space to achieve its tangent in the direction of the electric field vector at that point. Expert Answer. In pictorial form, an electric field describes the intensity of the field in front of it. 1 eV = 1.6 x 10 -19 joule. So, it would be equal to : $$\dfrac{\text{Work done}}{q} = K_eQ \Bigg ( \dfrac{1}{r_1} - \dfrac{1}{r_2} \Bigg )$$ I think that that should give the potential difference between two points in an . A mass is expressed as an internal energy stored in the object. The particles exert a force of attraction to move closer to each other in the presence of attractive forces. Furthermore, if the mass attached to the string is further stretched, the potential energy will be increased. The potential difference is the work done per unit charge as it moves from one point to another. The electric potential difference between two points is the work done per unit charge in moving a test charge from one point to the other. Voltmeter. As you move away from the charge, the potential decreases, and it actually increases, as the distance increases, also becoming closer and closer to zero. You are using an out of date browser. It also expl. You must select the board in which you will study the subject. The familiar term voltage is the common name for electric potential difference. When talking about potential difference in a circuit, whose work done are we talking about? In this step, you must first calculate the potential at any point x0 by integrating E*d*s along any path from x0 to x. $$\int_{r_1}^{r_2} K_e \dfrac{Qq}{r^2}dr$$ Both the magnitude of charge and the number of field lines are proportional to their magnitude. There are a few points to cover for this configuration: Default the camera if any settings are already incorrect. What does it mean to say that the potential difference between two points in an electric circuit is one Volt? The voltage between two points is equal to the work done per unit of charge that moves between those two points. Since dx is small, the electric field E is assumed to be uniform along AB. The electric potential energy of a charge determines the amount of effort required to relocate it from its original location to another. Making statements based on opinion; back them up with references or personal experience. capacitance. In the second case, B stands as the initial . The current density is equal to the current divided by the cross sectional area. Finally, calculate the potential difference between the two points by multiplying the electric field at each point by the distance between the two points. The equation for calculating the electric field from the potential difference is as follows: E = V/d where E is the electric field, V is the potential difference, and d is the distance between the two points. Energy is defined as the difference between a charged and a uniform sphere because a charged sphere has a distributed charge, whereas a uniform sphere has no distributed charge. For a better experience, please enable JavaScript in your browser before proceeding. Looking for a function that can squeeze matrices. The potential will be positive if the charge is on the outer surface of the sphere and negative if the charge is on the inner surface. Connecting three parallel LED strips to the same power supply, Examples of frauds discovered because someone tried to mimic a random sequence. You have no idea how confused I was because of this. How do I tell if this single climbing rope is still safe for use? The greater the distance between the heavenly bodies, the more potential energy they represent. The strength of the electric field at any point in space is determined by the amount of charge on the sphere. MathJax reference. Let me know if it's correct and if it isn't, why it's incorrect. kinetic energy of charge = charge x potential difference. Why is apparent power not measured in Watts? The Assam Board UP, Haryana Board, Himachal Pradesh Board, Jharkhand Board, Gujarat Board, Rajasthan Board, Tripura Board, and Uttarakhand Board are all part of the same entity. The potential difference between two points in an electric field is defined to be the work done to move a unit charge from one point to the other. On the other hand potential difference is defined as if a positive charge is taken from a point to another point in an electric field then the difference of the electric potential between the two points is called the potential difference. The Laplacian operator is the most common method for distinguishing potential functions with respect to distance, but many other methods exist. Positive charges, for example, have a greater potential than negative charges, and charges in the middle of an electric field have the same potential as charges in the center. As long as the electric potential is directed towards the center of the conductor, it always exceeds the potential at the conductors outer surface. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. JavaScript is disabled. Table of Content The electric field in a region is described as a vector quantity E; the same field can also be described as a scalar quantity V at each point of space. x)/((x*(2)&r*2)(3//2)) (field on axis of a ring at distance x)br> The number 4 is represented by the letter []. Positive and negative charges are always possible if you are infinitely distant from the charge. In an electric field, the potential difference between two points is proportional to the magnitude of the electric field. Solution. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, $$\int_{r_1}^{r_2} K_e \dfrac{Qq}{r^2}dr$$, $K_eQq \Bigg ( \dfrac{1}{r_1}-\dfrac{1}{r_2} \Bigg )$, $$\dfrac{\text{Work done}}{q} = K_eQ \Bigg ( \dfrac{1}{r_1} - \dfrac{1}{r_2} \Bigg )$$, Thank you so much! The SI unit of potential difference is the volt (V), which is equal to one joule per coulomb (J/C). The PDF Question Papers are free for off-the-shelf practice and can be accessed online. The potential difference between two points is the work done per unit charge in moving a charge between those points. The build-up of charge produces an electric field that extends from the surface of the conductor out into the surrounding space. The magnitude of charge is, .. :). The best answers are voted up and rise to the top, Not the answer you're looking for? Direction of arrows of a field line indicates the direction of the electric field, which is pointing upwards if there is a positive charge and downwards if there is a negative charge. An electric field (represented by an arrow) and two points (A and B) in the electric field are depicted in the diagrams. The electric field, which governs the movement of charges and currents, is critical to understanding electric fields. The potential difference is the product of the electric field and the distance between the two points. This is the type of electric field that nature produces. It is proportional to the work that has been performed to move a charge in a current field to obtain the electric potential energy of a charge. The SI unit of potential difference is the volt (V), which is equal to one joule per coulomb (J/C). Because the electric potential at the center of a conductor is always lower than the electric potential at the outer surface of a conductor, the electric potential at the outer surface is always greater than the electric potential at the center of the conductor. 1 volt= 1 joule/ 1 coulomb. Next, calculate the distance between the two points. 6.13 Potential difference between two points in a circuit from Office of Academic Technologies on Vimeo.. 6.13 Potential difference between two points in a circuit. The electric potential generated by a set of charges is the sum of potentials generated by each charge taken in isolation. Like the potential, in the International System of Units potential difference is measured in volts. the potential difference of zero between two or more positions in an electric field. The electric potential difference between two points A and B can be calculated in many different ways. The potential at the surface of a hemisphere is the potential difference between the top and bottom of the hemisphere. The electric potential of an electric field determines how much energy is required to move the charge. The potential difference between two points is also proportional to the distance between those points. 3. . As a result, the potential is the same as that of a point charge: The electric field in a conducting sphere is zero, so the potential remains constant at the surface at the same value as it was at the start: Potentials for other charge geometries. This work done is converted into kinetic energy of charge. The Higgs Field: The Force Behind The Standard Model, Why Has The Magnetic Field Changed Over Time. E=0B indicates that the electric and magnetic fields are related. Unit for measuring the potential difference is volt and . When an electric field line is not parallel to another, it is not always straight. Higher potentials require more energy to move a charge, which can cause an electric current to flow more slowly. rev2022.12.9.43105. The absence of an electric field in a conductor means that the entire conductor is connected at the same potential. Potential difference between and should be a big zero as we are moving perpendicular to the field and potential difference between and is so . It is denoted by d V. d V = d w d q. Potential difference is the difference between the potentials between two points in the electric field. Electric field as potential gradient. Because of the energy potential of the masses, the attraction between the two masses is an essential component of the potential energy of the mass due to the gravitational force. This charge would be similar to that found on one side of a flat plate if not. What happens if you score more than 99 points in volleyball? In this article, well go over the relationship between potential energy and distance. The potential difference between two points (1 and 2) of an electric field is equal to the work done by said field on the unit of positive charge to transport it from point 1 to point 2. How would you explain this to someone who doesnt know? To form an Electric Field, all rays must reach infinity before they can form the field. To find the potential difference between two points, first find the electric field at each point. It is a measure of the work done per unit charge by an electric field to move a charge from one point to another. Work done in moving the charge from A to B is. Is the hemisphere closed? Analog voltmeters move a pointer across a scale in proportion to the voltage measured and can be . To put it another way, the electric field is a vector field defined by the sum of the electric potential field and the normal field in space at any given point. The potential at a given point is still found by integrating the electric field, or equivalently, by adding up the potential contributions of all charges with Coulomb's law. The electric potential energy at a is always greater than the maximum energy at b, as long as the electric field exerts a force inversely proportional to the distance between charges. What is the center of the hemisphere electric field? How Solenoids Work: Generating Motion With Magnetic Fields. Are there conservative socialists in the US? How to smoothen the round border of a created buffer to make it look more natural? Because the electric field inside a conductor is always zero, it is always directed toward the center of a conductor. It is used to create an electric field. For example, every battery has two terminals, and its voltage is the potential difference between them. What are the electric and magnetic properties? The proportionality constant is the inverse of the permittivity of the medium. So the potential difference between two points in an electric field is a scalar quantity. When an electric field is present, charges can travel towards or away from it, and currents can flow in specific directions. The simplification of this integral, according to my Physics textbook is $K_eQq \Bigg ( \dfrac{1}{r_1}-\dfrac{1}{r_2} \Bigg )$. 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