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hitemup

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## Homework Statement

A thin circular ring of radius R has charge Q/2 uniformly distributed on the top half, and -Q/2 on the bottom half.

a) What is the value of the electric potential at a point a distance x along the axis through the center of the circle?

b) What can you say about the electric field E at a distance x along the axis. Let V = 0 at r = infinity.

## Homework Equations

Coulomb's Law

## The Attempt at a Solution

Since the electric potential is a scalar, the answer for the part a is simply zero.

But there is something confuses me in part b.

https://www.physicsforums.com/threads/electric-field-of-a-semi-circle-ring.799746/#post-5021977

This is what I drew for the flat ring problem while studying Coulomb's Law. As you see, dEsin(theta) was not equal to the y component of dE.

Now I have a solutions manual, and for part b, this is the answer.

(b) We follow Example 21-9 from the textbook. But because the upper and lower halves of the ring are oppositely charged, the parallel components of the fields from diametrically opposite infinitesimal segments of the ring will cancel each other,

**and the perpendicular components add, in the negative y direction.**We know then that E_x = 0 .

The solution continues with dEsin(theta) integrated from 0 to 2*pi*r

How can the perpendicular components be added even though they are not in the same direction? Shouldn't we do what we did for the semi-circle problem to find y component of the field?