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Electric Charges And Fields

Question

The force per unit length between two straight conductors separated by a distance of 0.02 m is 2 x 10^-3 N m^-1. The current in one conductor is 10 A and that in the other conductor is

20 A

5 A

2 A

10 A

Solution

20 A

Force per unit length between two parallel current carrying wire is given by

F = $\frac{μ_{0}}{2 π} \frac{I_{1} I_{2}}{r}$

Hence $\frac{μ_{0}}{4 π}$ = 10^-7 N m A^-2

r = 0.02 m

D = 2 × 10^-3 N m^-1

I₁ = 10 A

I₂ = ?

so, 2 × 10^-3 = 2 × 10^-7 × $\frac{10 \times I_{1}}{0.02}$

0.02 × 10⁴ = 10 I₁

∴ I₁ = 20 A