Question

4. In lecture we derived the electric field a distance z above the center of a thin ring of charge and a uniform disk of charge. Now determine the electric field a distance z above the center of a ring with charge uniformly distributed between an inner radius Ri and an outer rads R2 (alternatively, you can describe this as a disk of rads 2 with a circular hole of radius R). Do this two ways: by directly performing an integral over the surface of the ring and by superposition.

Answer 1

Ans

Integration method:

We can break the disk (with a hole) into rings. We use the expression of the electric field due to a ring in the disk. To get the total field we integrate over the disk from r= R₁ to r = R₂ .

Superposition method:

The electric field at z due to the disk of radius R₂ is the sum of the electric fields due to the disk with the hole and the disk of radius R₁ . Using this we find the electric field at z due to the annular disk.

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