Question

Two long, parallel wires are separated by a distance of 2.50 cm. The force per unit length that each wire exerts on the other is 4.00 × 10 N/m, and the wires repel each other. The current in one wire is 0.600 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:

The current in the second wire is 8.33 A and the two currents are flowing in the opposite directions

Explanation:

Given that,

The separation between two long parallel wires, d = 2.5 cm

The force per unit length that each wire exerts on the other is, $\dfrac{F}{l}=4\times 10^{-5}\ N/m$

The current in one wire, $I_1=0.6\ A$

(a) The force per unit length of the wire is given by :

$\dfrac{F}{l}=\dfrac{\mu_oI_1I_2}{2\pi r}$

On putting all the values we get :

$4\times 10^{-5}=\dfrac{4\pi \times 10^{-7}\times 0.6I_2}{2\pi \times (2.5\times 10^{-2})}$

$I_2=8.33\ A$

So, the current in the second wire is 8.33 A.

(b) It is given that, both the wires repel each other, so the current in other wire is flowing in the opposite direction of the current in the first wire.

Hence, this is the required solution.