Timeline for Energy due image charges
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2023 at 0:50 | comment | added | Aditya Agarwal | You can also consider the work done by an electric field for a charge configuration. $$\int_\limits{\mathbb{R^{3}}} \frac{\epsilon_{0}}{2} E^{2} dV.$$ If we consider the electric field produced by the infinite plane, it is only due to the side which has the charge. And the other-side of the plane would not have any charges(because if there was any charge then they would exert force on each other and then they would get as far away as possible to minimise the interaction between them.) So you can do the integral and find that it is 1/2 of the value with the image charges. | |
| Mar 9, 2023 at 0:19 | comment | added | user35013 | If I somehow set the charges on the plane first - generating a potential $V$ on the position the real charge is going to be - the charge does not aquire a potential energy of $qV$? How do I justify the factor $1/2$ mathematically (other than a physical consideration)? | |
| Mar 8, 2023 at 23:55 | history | answered | Aditya Agarwal | CC BY-SA 4.0 |