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32-667: (Redirected from Epe ) [REDACTED] Look up epe in Wiktionary, the free dictionary. Epe or EPE may refer to: Places [ edit ] Epe, North Rhine-Westphalia , Germany Epe, Netherlands Epe, Lagos , Nigeria Eastern Peripheral Expressway , National Capital Region, India Science [ edit ] Electric potential energy Elvis Presley Enterprises , an American entertainment company England's Past for Everyone , an English historical research project Ephenidine European Parliament of Enterprises ,

64-531: A business organization Everyday Practical Electronics , a British hobbyist magazine Expanded polyethylene Extrasolar Planets Encyclopaedia , an online database of exoplanets End-Permian Extinction , a mass extinction at the end of the Paleozoic See also [ edit ] Épée , a weapon used in sport fencing Treaty of Epe Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with

96-475: A business organization Everyday Practical Electronics , a British hobbyist magazine Expanded polyethylene Extrasolar Planets Encyclopaedia , an online database of exoplanets End-Permian Extinction , a mass extinction at the end of the Paleozoic See also [ edit ] Épée , a weapon used in sport fencing Treaty of Epe Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with

128-415: A system containing only one point charge is zero, as there are no other sources of electrostatic force against which an external agent must do work in moving the point charge from infinity to its final location. A common question arises concerning the interaction of a point charge with its own electrostatic potential. Since this interaction doesn't act to move the point charge itself, it doesn't contribute to

160-423: A system of n charges q 1 , q 2 , …, q n at positions r 1 , r 2 , …, r n respectively, is: U E = 1 2 ∑ i = 1 n q i V ( r i ) . {\displaystyle U_{\mathrm {E} }={\frac {1}{2}}\sum _{i=1}^{n}q_{i}V(\mathbf {r} _{i}).} The electrostatic potential energy of

192-460: Is set to zero when r ref is infinity: U E ( r r e f = ∞ ) = 0 {\displaystyle U_{E}(r_{\rm {ref}}=\infty )=0} so U E ( r ) = − ∫ ∞ r q E ⋅ d s {\displaystyle U_{E}(r)=-\int _{\infty }^{r}q\mathbf {E} \cdot \mathrm {d} \mathbf {s} } When

224-559: Is the distance between q i and q j . The electrostatic potential energy U E stored in a system of two charges is equal to the electrostatic potential energy of a charge in the electrostatic potential generated by the other. That is to say, if charge q 1 generates an electrostatic potential V 1 , which is a function of position r , then U E = q 2 V 1 ( r 2 ) . {\displaystyle U_{\mathrm {E} }=q_{2}V_{1}(\mathbf {r} _{2}).} Doing

256-948: Is the distance between charge Q i and Q j . If we add everything: U E = 1 2 1 4 π ε 0 [ Q 1 Q 2 r 12 + Q 1 Q 3 r 13 + Q 2 Q 1 r 21 + Q 2 Q 3 r 23 + Q 3 Q 1 r 31 + Q 3 Q 2 r 32 ] {\displaystyle U_{\mathrm {E} }={\frac {1}{2}}{\frac {1}{4\pi \varepsilon _{0}}}\left[{\frac {Q_{1}Q_{2}}{r_{12}}}+{\frac {Q_{1}Q_{3}}{r_{13}}}+{\frac {Q_{2}Q_{1}}{r_{21}}}+{\frac {Q_{2}Q_{3}}{r_{23}}}+{\frac {Q_{3}Q_{1}}{r_{31}}}+{\frac {Q_{3}Q_{2}}{r_{32}}}\right]} Finally, we get that

288-941: Is the distance between the point charges q and Q i , and q and Q i are the assigned values of the charges. The electrostatic potential energy U E stored in a system of N charges q 1 , q 2 , …, q N at positions r 1 , r 2 , …, r N respectively, is: U E = 1 2 ∑ i = 1 N q i V ( r i ) = 1 2 k e ∑ i = 1 N q i ∑ j ≠ i j = 1 N q j r i j , {\displaystyle U_{\mathrm {E} }={\frac {1}{2}}\sum _{i=1}^{N}q_{i}V(\mathbf {r} _{i})={\frac {1}{2}}k_{e}\sum _{i=1}^{N}q_{i}\sum _{\stackrel {j=1}{j\neq i}}^{N}{\frac {q_{j}}{r_{ij}}},} where, for each i value, V( r i )

320-2249: Is the electric potential in r 1 created by charges Q 2 and Q 3 , V ( r 2 ) {\displaystyle V(\mathbf {r} _{2})} is the electric potential in r 2 created by charges Q 1 and Q 3 , and V ( r 3 ) {\displaystyle V(\mathbf {r} _{3})} is the electric potential in r 3 created by charges Q 1 and Q 2 . The potentials are: V ( r 1 ) = V 2 ( r 1 ) + V 3 ( r 1 ) = 1 4 π ε 0 Q 2 r 12 + 1 4 π ε 0 Q 3 r 13 {\displaystyle V(\mathbf {r} _{1})=V_{2}(\mathbf {r} _{1})+V_{3}(\mathbf {r} _{1})={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q_{2}}{r_{12}}}+{\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q_{3}}{r_{13}}}} V ( r 2 ) = V 1 ( r 2 ) + V 3 ( r 2 ) = 1 4 π ε 0 Q 1 r 21 + 1 4 π ε 0 Q 3 r 23 {\displaystyle V(\mathbf {r} _{2})=V_{1}(\mathbf {r} _{2})+V_{3}(\mathbf {r} _{2})={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q_{1}}{r_{21}}}+{\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q_{3}}{r_{23}}}} V ( r 3 ) = V 1 ( r 3 ) + V 2 ( r 3 ) = 1 4 π ε 0 Q 1 r 31 + 1 4 π ε 0 Q 2 r 32 {\displaystyle V(\mathbf {r} _{3})=V_{1}(\mathbf {r} _{3})+V_{2}(\mathbf {r} _{3})={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q_{1}}{r_{31}}}+{\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q_{2}}{r_{32}}}} Where r ij

352-441: Is the electrostatic potential due to all point charges except the one at r i , and is equal to: V ( r i ) = k e ∑ j ≠ i j = 1 N q j r i j , {\displaystyle V(\mathbf {r} _{i})=k_{e}\sum _{\stackrel {j=1}{j\neq i}}^{N}{\frac {q_{j}}{r_{ij}}},} where r ij

SECTION 10

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384-404: Is the separation between the two point charges. The electrostatic potential energy of a system of three charges should not be confused with the electrostatic potential energy of Q 1 due to two charges Q 2 and Q 3 , because the latter doesn't include the electrostatic potential energy of the system of the two charges Q 2 and Q 3 . The electrostatic potential energy stored in

416-451: Is used to describe the potential energy in systems with time-variant electric fields , while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields. The electric potential energy of a system of point charges is defined as the work required to assemble this system of charges by bringing them close together, as in the system from an infinite distance. Alternatively,

448-407: The curl ∇ × E is zero, the line integral above does not depend on the specific path C chosen but only on its endpoints. This happens in time-invariant electric fields. When talking about electrostatic potential energy, time-invariant electric fields are always assumed so, in this case, the electric field is conservative and Coulomb's law can be used. Using Coulomb's law , it is known that

480-414: The electrostatic field of a continuous charge distribution is: u e = d U d V = 1 2 ε 0 | E | 2 . {\displaystyle u_{e}={\frac {dU}{dV}}={\frac {1}{2}}\varepsilon _{0}\left|{\mathbf {E} }\right|^{2}.} One may take the equation for the electrostatic potential energy of

512-846: The change in electrostatic potential energy, U E , of a point charge q that has moved from the reference position r ref to position r in the presence of an electric field E is the negative of the work done by the electrostatic force to bring it from the reference position r ref to that position r . U E ( r ) − U E ( r r e f ) = − W r r e f → r = − ∫ r r e f r q E ⋅ d s . {\displaystyle U_{E}(r)-U_{E}(r_{\rm {ref}})=-W_{r_{\rm {ref}}\rightarrow r}=-\int _{{r}_{\rm {ref}}}^{r}q\mathbf {E} \cdot \mathrm {d} \mathbf {s} .} where: Usually U E

544-499: The charges (not the absolute values of the charges—i.e., an electron would have a negative value of charge when placed in the formula). The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula. The electrostatic force F acting on a charge q can be written in terms of the electric field E as F = q E , {\displaystyle \mathbf {F} =q\mathbf {E} ,} By definition,

576-1125: The electric field is given by | E | = E = 1 4 π ε 0 Q s 2 {\displaystyle |\mathbf {E} |=E={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{s^{2}}}} and the integral can be easily evaluated: U E ( r ) = − ∫ ∞ r q E ⋅ d s = − ∫ ∞ r 1 4 π ε 0 q Q s 2 d s = 1 4 π ε 0 q Q r = k e q Q r {\displaystyle U_{E}(r)=-\int _{\infty }^{r}q\mathbf {E} \cdot \mathrm {d} \mathbf {s} =-\int _{\infty }^{r}{\frac {1}{4\pi \varepsilon _{0}}}{\frac {qQ}{s^{2}}}{\rm {d}}s={\frac {1}{4\pi \varepsilon _{0}}}{\frac {qQ}{r}}=k_{e}{\frac {qQ}{r}}} The electrostatic potential energy, U E , of one point charge q in

608-640: The electric potential as follows: U E ( r ) = q V ( r ) {\displaystyle U_{\mathrm {E} }(\mathbf {r} )=qV(\mathbf {r} )} The SI unit of electric potential energy is joule (named after the English physicist James Prescott Joule ). In the CGS system the erg is the unit of energy, being equal to 10 Joules. Also electronvolts may be used, 1 eV = 1.602×10 Joules. The electrostatic potential energy, U E , of one point charge q at position r in

640-840: The electric potential energy of any given charge or system of charges is termed as the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration. U E ( r ) = − W r r e f → r = − ∫ r r e f r q E ( r ′ ) ⋅ d r ′ {\displaystyle U_{\mathrm {E} }(\mathbf {r} )=-W_{r_{\rm {ref}}\rightarrow r}=-\int _{{\mathbf {r} }_{\rm {ref}}}^{\mathbf {r} }q\mathbf {E} (\mathbf {r'} )\cdot \mathrm {d} \mathbf {r'} } The electrostatic potential energy can also be defined from

672-660: The electrostatic force F and the electric field E created by a discrete point charge Q are radially directed from Q . By the definition of the position vector r and the displacement vector s , it follows that r and s are also radially directed from Q . So, E and d s must be parallel: E ⋅ d s = | E | ⋅ | d s | cos ⁡ ( 0 ) = E d s {\displaystyle \mathbf {E} \cdot \mathrm {d} \mathbf {s} =|\mathbf {E} |\cdot |\mathrm {d} \mathbf {s} |\cos(0)=E\mathrm {d} s} Using Coulomb's law,

SECTION 20

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704-724: The electrostatic potential energy stored in the system of three charges: U E = 1 4 π ε 0 [ Q 1 Q 2 r 12 + Q 1 Q 3 r 13 + Q 2 Q 3 r 23 ] {\displaystyle U_{\mathrm {E} }={\frac {1}{4\pi \varepsilon _{0}}}\left[{\frac {Q_{1}Q_{2}}{r_{12}}}+{\frac {Q_{1}Q_{3}}{r_{13}}}+{\frac {Q_{2}Q_{3}}{r_{23}}}\right]} The energy density, or energy per unit volume, d U d V {\textstyle {\frac {dU}{dV}}} , of

736-604: The formula given in ( 1 ), the electrostatic potential energy of the system of the three charges will then be: U E = 1 2 [ Q 1 V ( r 1 ) + Q 2 V ( r 2 ) + Q 3 V ( r 3 ) ] {\displaystyle U_{\mathrm {E} }={\frac {1}{2}}\left[Q_{1}V(\mathbf {r} _{1})+Q_{2}V(\mathbf {r} _{2})+Q_{3}V(\mathbf {r} _{3})\right]} Where V ( r 1 ) {\displaystyle V(\mathbf {r} _{1})}

768-598: The 💕 (Redirected from Epe ) [REDACTED] Look up epe in Wiktionary, the free dictionary. Epe or EPE may refer to: Places [ edit ] Epe, North Rhine-Westphalia , Germany Epe, Netherlands Epe, Lagos , Nigeria Eastern Peripheral Expressway , National Capital Region, India Science [ edit ] Electric potential energy Elvis Presley Enterprises , an American entertainment company England's Past for Everyone , an English historical research project Ephenidine European Parliament of Enterprises ,

800-455: The presence of n point charges Q i , taking an infinite separation between the charges as the reference position, is: U E ( r ) = q 4 π ε 0 ∑ i = 1 n Q i r i , {\displaystyle U_{E}(r)={\frac {q}{4\pi \varepsilon _{0}}}\sum _{i=1}^{n}{\frac {Q_{i}}{r_{i}}},} where r i

832-444: The presence of a point charge Q , taking an infinite separation between the charges as the reference position, is: U E ( r ) = 1 4 π ε 0 q Q r {\displaystyle U_{E}(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}{\frac {qQ}{r}}} where r is the distance between the point charges q and Q , and q and Q are

864-442: The same calculation with respect to the other charge, we obtain U E = q 1 V 2 ( r 1 ) . {\displaystyle U_{\mathrm {E} }=q_{1}V_{2}(\mathbf {r} _{1}).} The electrostatic potential energy is mutually shared by q 1 {\displaystyle q_{1}} and q 2 {\displaystyle q_{2}} , so

896-679: The stored energy of the system. Consider bringing a point charge, q , into its final position near a point charge, Q 1 . The electric potential V( r ) due to Q 1 is V ( r ) = k e Q 1 r {\displaystyle V(\mathbf {r} )=k_{e}{\frac {Q_{1}}{r}}} Hence we obtain, the electrostatic potential energy of q in the potential of Q 1 as U E = 1 4 π ε 0 q Q 1 r 1 {\displaystyle U_{E}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {qQ_{1}}{r_{1}}}} where r 1

928-545: The system of three charges is: U E = 1 4 π ε 0 [ Q 1 Q 2 r 12 + Q 1 Q 3 r 13 + Q 2 Q 3 r 23 ] {\displaystyle U_{\mathrm {E} }={\frac {1}{4\pi \varepsilon _{0}}}\left[{\frac {Q_{1}Q_{2}}{r_{12}}}+{\frac {Q_{1}Q_{3}}{r_{13}}}+{\frac {Q_{2}Q_{3}}{r_{23}}}\right]} Using

960-482: The title EPE . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=EPE&oldid=1222407672 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages epe From Misplaced Pages,

992-524: The title EPE . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=EPE&oldid=1222407672 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Electric potential energy The term "electric potential energy"

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1024-447: The total stored energy is U E = 1 2 [ q 2 V 1 ( r 2 ) + q 1 V 2 ( r 1 ) ] {\displaystyle U_{E}={\frac {1}{2}}\left[q_{2}V_{1}(\mathbf {r} _{2})+q_{1}V_{2}(\mathbf {r} _{1})\right]} This can be generalized to say that the electrostatic potential energy U E stored in

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