: Consider a thin disc of radius R o placed in the xy-plane. The disc has a hole

Question

: Consider a thin disc of radius Ro placed in the xy-plane. The disc has a hole of radius Ri in the middle. [It is basically a washer.] The uniform surface charge density is > 0 (a constant). The washer centered on the z-axis.

(a) Draw a clear diagram of the situation and inlude any quantities you use throughout the rest of the problem. 2

(b) What is the area on washer?

(c) What are the units of ?

(d) What is the total charge on the washer?

(e) Starting with the expression for the electric field of ring of charge (either from you notes or the text), find the electric field on the z-axis at a distance b above the plane. Carry out all the integrals and give a clean expression for the final answer.

(f) By taking the limit where b is much larger than Ro, show that that far way, the field behaves approximately like that of a point charge.

(g) Suppose the washer is not uniformly charged, but has (r) = o r where r is the radius measured from the center of the disk. Find the total charge on the washer.

(h) find the electric field on the z-axis at a distance b above the xy-plane. The integral you encounter will be more difficult than in part e, so feel free to look it up in an integral table.

Explanation / Answer

(b) Area on the washer = pi (Ro^2 - Ri^2)

(c) Units of = C/m^2

(d) Total charge on the washer = pi (Ro^2 - Ri^2)

(e)Electric field = 2 pi k (1 - b / sqrt(b^2 + Ro^2))

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