Question

A long copper wire with radius of 1.0 mm carries a uniform surface charge density of 5.0 x 10^-6 C/m². 

a. Find the total charge in a 1.0-meter-long section of the wire. 

b.. Find the magnitude of the electric field at a distance of 15 cm from the wire. 

Answer 1

a. Find the total charge in a 1.0-meter-long section of the wire. First, determine the area:

$$A=\pi rL.$$

The total charge:

$$Q=\sigma A=\sigma \pi r L=1.57·10^{-8}\text{ C}.$$

b. Since the length is infinite, and the radius is 150 smaller than the distance, the field is

$$B=\frac{\mu_0 I}{2\pi R}=\frac{\mu_0 Q/t}{2\pi R}=\frac{2.09·10^{-14}}{t}\text{ T},$$

where t - time required for the charge Q to move in the wire.