Question

A wire lies along the z axis and carries current I = 23 A in the positive z direction. A small conducting sphere of radius R = 2 cm is initially at rest on the y axis at a distance h = 49 m above the wire. The sphere is dropped at time t = 0. Assume that the only magnetic field is that produced by the wire.

(a) What is the electric field at the center of the sphere at t = 3 s?
mV/m
Direction

(b) What is the voltage across the sphere at t = 3 s?
= µV

Answer 1

a] Use v = u + gt

at t = 3s

v = 0 + 9.8(3) = 29.4 m/s

and y = 49 - (1/2)gt² = 49 - 4.9(3)² = 4.9 m.

this is the speed of the sphere at t = 3s and it is in the downward direction.

The magnetic field strength can be found using Ampere's law with r = y

the electric field at the center will then simply be:

= 27.6 x 10^-6 V/m.

this is the magnitude of the electric field and the direction can be found using the right hand rule and it comes out to be in the positive z direction.

b]

Potential difference will be due to the potential on the upper and lower surfaces of the sphere

V = Ed

d = diameter of the sphere

V = 110.4 x 10^-6 V.