Question

A straight, cylindrical wire lying along the x axis has a length of 0.500 m and a diameter of 0.200 mm. it is made of a meterial described by Ohm's law with a with a resistivity of p=4.00 *10^-8 Ohm . m. Assume a potential of 4.00 V is maintained at the left end of the wire at x=0. Also assume V=0 at x=0.500 m. Find a) the magnitude and direction of the electric field in the wire , b) the resistance of the wire, c) the magnitude direction of the electric current in the wire, and d) the current density in the wire. e) Show that E=pJ

Answer 1

a)

$$E=\frac{4-0}{0.5-0}=8.00\frac{V}{m}$$

Direction: rightwards (positive x-direction).

b)

$$R=4.00\cdot10^{-8} \frac{0.5}{0.25\pi(0.0002)^2}=0.637\Omega$$

c) Direction: rightwards (positive x-direction).

$$I=\frac{V}{R}=\frac{4}{0.637}=6.28\ A$$

d)

$$J=\frac{6.28}{0.25\pi(0.0002)^2}=2.00\cdot 10^8\frac{A}{m^2}$$

e)

$$E=\rho J=(4.00\cdot10^{-8})(2.00\cdot 10^8)=8.00\frac{V}{m}$$