A straight, cylindrical wire lying along the x axis has a length of 0.495 m and

Question

A straight, cylindrical wire lying along the x axis has a length of 0.495 m and a diameter of 0.225 mm. It is made of a material described by Ohm's law with a resistivity of rho=4.00 times 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=0.495 m. Find the magnitude and direction of the electric field in the wire. Find the resistance of the wire. Find the magnitude and direction of the electric current in the wire. Find the current density in the wire.

Explanation / Answer

a) magnitude of electric field is E= V/d = 4/(0.495) = 8.08 V/m

direction is from x = 0 to x = 0.495

b) resistance is R = rho*l/A = (4*10^-8*0.495)/(3.142*(0.225/2)^2*10^-6) = 0.497 ohm

C) electric current is i = V/R = 4/0.497 = 8.04 A

direction of current is from x = 0 to x = 0.495

d) current density is j = i/A = 8.04/(3.142*(0.225/2)^2*10^-6) = 2.02*10^8 A/m^2

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