Question

A circular annulus of inner radius r and outer radius R has a uniform charge density a. What will be the total charge on the annulus?

(a) a*(R^2-r^2)

(b) π*a*(R^2-r^2)

(c) a*(R-r)

(d) π*a* R^2

This question was addressed to me in final exam.

My question comes from Continuous Charge Distribution topic in chapter Charges and Fields of Physics – Class 12

Answer 1

Right answer is (b) π*a*(R^2-r^2)

For explanation I would say: Total surface area of the annulus = π*(R^2-r^2) because it has outer radius R and inner radius r. We know surface charge density is the amount of charge stored on the unit surface area. In this case, surface charge density is a. Therefore total charge on the annulus = π*a*(R^2-r^2).