A positive charge +q is located at the origin and a negatively charged ring is p

Question

A positive charge +q is located at the origin and a negatively charged ring is placed in the xy-plane as shown in the figure above. The total charge on the ring is ?q and is uniformly distributed

.

(a) Find the electric potential at point P on the positive z-axis. Simplify your answer by taking the limit of z ? R.

(b) Find the electric field using the electric potential found in (a). (In the z ? R limit) Specify both the magnitude and the direction. Compare your answer with the electric field due to a point charge or an electric dipole.

Explanation / Answer

https://docs.google.com/viewer?a=v&q=cache:9cOXAoZ6iKMJ:www.phys.uri.edu/~gerhard/PHY204/tsl81.pdf+&hl=en&gl=in&pid=bl&srcid=ADGEESi48pRCqbuMvtopfwZDYKEwkLiAKv9KW_A5jXr87ezYy9XvBdTm3WFrh21wmtCiMm-xcViIwk4AdcpSZEtkNgAFvA_n_z-z8SIqn_EFQwmnAQ2vIcs4M34vTLGs8IKBLOBzUtso&sig=AHIEtbSFwM5qV3mubYANU8-pH1DuSF7B2w

(V = kq/z + k(-q)/sqrt{z^2 + R^2}) ans.

for z>>R

V = kq/z + k(-q)/z = 0

E =-dV/dz = kq/z^2 + k(-q)*2z/2(z^2 + R^2)^3/2

E = kq/z^2 - kq*2z/2(z^2 + R^2)^3/2

E = kq/z^2 -kqz/(z^2 + R^2)^3/2 ans.

for z>>R

E = 0

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