A total charge of Q is deposited on a solid metal sphere of radius R. This charg

Question

A total charge of Q is deposited on a solid metal sphere of radius R. This charge distributes itself uniformly over the surface, yielding an electrostatic field = ( sigma /epsilon0) just outside the sphere and = 0 everywhere inside the sphere, where sigma = Q/4piR2 and is the outward pointing unit normal vector. Consider a small patch of surface area dA. We wish to calculate the electrostatic pressure P on this patch due to all the other surface charge. This pressure equals the electrostatic force per unit area, P = (dq)E/dA = sigma E, where E is the electrostatic field acting on the patch due to all the other charges. But what value of E do we use? (The total field is zero just inside the surface, but jumps to a nonzero value just outside the surface.) This problem addresses that question. Consider the small patch alone. What are the fields patch that the patch produces just outside and just inside the sphere? (Write these fields as vectors involving sigma and .) Hint: If you are infinitesimally close to the patch, even this small patch will look like an infinite sheet of charge. According to the superposition principle, the total field just outside the surface must equal a contribution from the patch itself plus a contribution other from all the other charge. What is other just outside the surface? (Again, write the result in terms of sigma and .)

Explanation / Answer

1) the electric field just inside the sphere will be / and just outside will be zero

2) yes it must be the Eother =-/

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