Question

A point charge -q is located at the origin. The point charge is surrounded by a ring with uniform line charge density λ and radius a. The charged ring sits in the x-y plane and is centered on the origin.

a) Calculate the electric potential along the z-axis using a reference point at ∞ using Coulomb’s law for V. (i.e. do not find the electric field first.)

b) Use E = −∇V to calculate the electric field along the z-axis.

c) you used symmetry to say that the x and y components of the electric field were zero. If the line charge formed a half circle instead of a full circle, then the x and y components would no longer be zero. Describe how you would modify the calculation of the electric potential (part a) so that the gradient (part b) would yield the correct electric field.

Answer 1