Question

Two long, parallel wires are separated by a distance of 3.30 cm. The force per unit length that each wire exerts on the other is 5.00×10−5 N/m, and the wires repel each other. The current in one wire is 0.620 A.
a. What is the current in the second wire?
b. Are the two currents in the same direction or in opposite directions?

Answer 1

Answer with Explanation:

We are given that

Distance between two parallel long wires=r=3.3 cm=$\frac{3.3}{100}=0.033m$

1 m=100 cm

$\frac{F}{l}=5\times 10^{-5} N/m$

$I_1=0.62 A$

a.We have to find the current in the second wire.

We know that

$\frac{F}{l}=\frac{2\mu_0I_1I_2}{4\pi r}$

Using the formula

$5\times 10^{-5}=\frac{2\times 10^{-7}\times 0.62\times I_2}{0.033}$

Where $\frac{\mu_0}{4\pi}=10^{-7}$

$I_2=\frac{5\times 10^{-5}\times 0.033}{2\times 10^{-7}\times 0.62}$

$I_2=13.3 A$

Hence, the current in the second wire=13.3 A

b.We are given that the wires repel each other.When the current carrying in the wires in opposite direction then, the wires repel to each other.

Hence,the two  currents in opposite directions.