Solution
a)
Potential at the center for half annulus ring can be given by Potential due to half disk of radius r2- potential due to half disk of radius r1
we know for a semi circular disk of radius r and surface charge density is given by
b)
To find electric field
We assume a thin semi circular ring of radius a and thickness da from the center and charge dQ
we know,
Electric field due to semi circular ring of radius 'a' is given by,
This can also be derived by taking a semi circular ring and find the electric field by integrating assumed point charges on the rod. proof given below
Now,
For the ring assumed
and
So, to get the electric field of the semi annular disk.
No, we cannot directly use the result of a) to get b) because E=dV/dr is applicable for point charges only. For these kind of bodies we need to find potential of its elements and then integrate it to get the answer.
If any doubt feel free to comment.
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