A ring with radius R and a uniformly distributed total charge Q lies in the xy p

Question

A ring with radius R and a uniformly distributed total charge Q lies in the xy plane, centered at the origin. Part A What is the potential V(z) due to the ring on the z axis as a function of z? Express your answer in terms of Q, z, R, and elementof_0 or k = 1/4 pi elementof_0. Part B What is the magnitude of the electric field E on the z axis as a function of z, for z > 0? Express your answer in terms of some or all of the quantities Q, z, R, and elementof_0 or k = By symmetry, the electric field has only one Cartesian component. In what direction does the electric field point? i j k

Explanation / Answer

(A) every part of ring is equidistant from given point,

so V = k Q / r

and r^2 = R^2 + z^2

V = k Q / sqrt[ R^2 + z^2]

(b) E = k Q / r^2 cos(theta)

cos(theta) = z / r

E = k Q z / r^3

E = k Q z / (R^2 + z^2)^(3/2) .......Ans

direction -> k

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