A) Determine an expression for the electric potential at the surface of the thin

Question

A) Determine an expression for the electric potential at the surface of the thin spherical shell ( when r=R, assuming V=0 at infinity)? Express your answer in terms of givens such as Q, R, q, and m.

B) Determine an expression for the electric potential energy for the system of two charges when the charge -q reaches the surface of the spherical shell (when r=R)? Express your answer in terms of givens such as Q, R, q, and m.

C) How fast will the charge -q be traveling when it reaches the surface r=R of the spherical shell. Express your answer in terms of the quanitites such as Q, R, q, and m.

D) Include a sketch and explain your starting assumptions for part D.

-q A negative point charge -q with mass m is released from rest at an extremely large distance (infinity) from a hollow thin spherical shell of positive charge QO and radius R which stays fixed in space. The charge -q accelerates toward the center of the shell due to electrostatic attraction between the charges. Assume electric potential of the thin shell is set to zero at infinity as usual. Let r represent the distance of the charge -q from the center of the spherical shell.

Explanation / Answer

a) Electric potential at the surafce = kQ / R

b) Electric PE = - kQq / R

c) when charge at infinity .
PE = 0 , KE = 0

when it reaches at r = R,

PE = - kQq/R , KE = mv^2 /2

using enenrgy conservation,

0 + 0 = - kQq/R + mv^2 /2

v = sqrt[ 2kQq / mR ]

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