- #1

wam_mi

- 81

- 1

## Homework Statement

(Part 1) A hoop of charge of radius k lies in the y, z plane, centred on the x axis, so that

it occupies the points (0, y, z) with y^2 + z^2 = k^2. If the (linear) charge density

in the hoop is j, calculate the electrostatic potential Fi at all points on the

x axis, and show that, far from the hoop on the x axis, Fi (x, 0, 0) = (2*pi*j)/|x|.

Explain briefly why this result was only to be expected.

(Part 2) More generally, what do you expect the leading behaviour of Fi(r) to be, far

from the hoop? (You do not need to give any detailed calculations.) Use your

answer to deduce the limiting forms of the equipotential surfaces and field lines,

again far from the hoop.

## Homework Equations

## The Attempt at a Solution

(Part 1)

Total Charge Q = Integrating j * dl with interval [0 , 2*pi]

= 2*pi*k*j

By Symmetry, Fi (x) = 2*pi*k*j / |x| (Is this wrong?)

And now I'm stuck for the rest of the question.

Please help! Thank you!