2022 Current ElectricityDrift of Electrons and Current Density Medium Question 28 of 130 in Current Electricity

A copper wire of length 10 m and radius $(10^{-2}/\sqrt{\pi})$ m has electrical resistance of $10\ \Omega$. The current density in the wire for an electric field strength of $10\ V/m$ is :

A $10^5\ A/m^2$
B $10^4\ A/m^2$
C $10^6\ A/m^2$
D $10^{-5}\ A/m^2$

The answer is A.

Solution

Radius of wire $r = \frac{10^{-2}}{\sqrt{\pi}}$ m, so area $A = \pi r^2 = 10^{-4}\ m^2$ $j = \frac{i}{A} = \frac{V}{R}\cdot\frac{1}{A} = \frac{E\ell}{RA}$ $j = \frac{10 \times 10}{10 \times 10^{-4}} = 10^5\ A/m^2$

Concept current density from resistance and field

Current Electricity in past papers

130 questions from this chapter have appeared across 27 exam years.