Gwen Stacy to the rescue!

Electricity and Magnetism Level 4

The evil Electro has caught Spidey and has put him in a spherical metallic cage of radius 'R'. Eventually, Electro decides to take some nap after his awesome fight with Spidey. He ties Spidey to a non conducting pole At the center of the metallic cage and dozes off to sleep at some distance 'a' besides Spidey. Spidey with his agility manages to break off from the pole but in order to escape from the cage he must bring the potential of the cage to zero in order to avoid an electric shock. (The spherical metallic cage acquires a potential due to the charge on Electro 'Q')

On the other hand Gwen Stacy tries to help her boyfriend. She borrows a charge accumulator from her scientist friend and tries to bring the cage's potential to zero. For this she needs to know how much charge she must accumulate and where from Spidey should she stand in order to do so.

Can you help this pretty lady rescue her friend?

Details and assumptions

Take $a = \frac{R}{2}$

3R/2 , -2Q/3 3R/2 , --Q/3 2R , -Q/3 2R , -2Q/3

1 solution

Pinak Wadikar
Jun 23, 2014

This problem can be solved by 'Method of Images'

Let us assume a charge 'q' at a distance 'r' from the center of the cage.
Due to this charge the potential at the spherical shell must be zero.

Using this we obtain two equations.

$\frac{kq}{r-R} + \frac{kQ}{a+R} = 0$

$\frac{kq}{r+R} + \frac{kQ}{R-a} = 0$

Using these two equations and $a = \frac{R}{2}$ we get the two unknowns 'r' and 'q'.

Gwen Stacy to the rescue!

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