Consider the semicircle as a strip with varying width according to

and also has uniform surface distribution with

Let Ex be the electrical field at point P which is parallel to its diameter.If we have many same strips, we can arrange it become a ball with the same radius. See picture below.
(sorry, incomplete picture, it's hard to make a complete picture, but I hope you understand)

The ball is consists of many strips, so we can use superposition concept to determine the electrical field at point P.
Because all of the strips are symmetric to diameter of the ball, we can say that the electrical field at point P is

where N is number of the strips.

As we know, no electrical field inside a uniform charged ball, so

means there's no electrical field parallel to the diameter. So we can say that electrical potential along its diameter is the same. So,

That's my solution.
If you have any question, correction, or comment, please leave a comment below.
Thank you.

Solution - Semicircle Charged ArcSocialTwist Tell-a-Friend


mustafa said... @ December 24, 2009 at 5:20 AM

the solution overlooked the fact that Ep= N Ex requires vector sum of Ex.Agreed that Ep=0 for shielding case..it doesn't mean that Ex =0. Since, Ex because of one ring cancels out the Ex of the ring exacly opposite to it.

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