A non-conducting charged sheet and a non-conducting sphere (radius b) are arrang

Question

A non-conducting charged sheet and a non-conducting sphere (radius b) are arranged as shown b in the figure. The right-most surface of the sheet is at x = 0 and the center of the sphere is on the x-axis at x = x0. The sheet has a positive uniform charge density a while the sphere is uniformly charged with total negative charge - q (where q itself is positive). Answer the following questions regarding the electric field E rightarrow (x) and the electrostatic potential V(x). Using proper unit-vector notation, write down the appropriate expression for E rightarrow (x) at point P. V(x) = - sigma / 4 eplision 0 s2 - kq / (x0 - x) Determine whether the following What must V(x) be so that it gives E rightarrow (x) at point P and is also zero at the surface of the plane (i. e. , V(0) = 0)? Verify your answer with an appropriate integral.

Explanation / Answer

a)

E = /20 + kq/(x0 - x)2

b)

E(x) = -(dV(x))/dx = x/20 + kq/(x0-x)2

Therefore this V(x) does not give E(x).

c)

V(x) = -E.dx = -(/20 + kq/(x0 - x)2)dx = -x/20 - kq/(x0 - x)

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