Question

A vertical straight wire carrying an upward 24-A current exerts an attractive force per unit length of 88 X 104N/m on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?

Answer 1

Answer:

The current flows in the second wire is $1.3\times10^{10}\ A$

Explanation:

Given that,

Upward current = 24 A

Force per unit length$\dfrac{F}{l} =88\times10^{4}\ N/m$

Distance = 7.0 cm

We need to calculate the current in second wire

Using formula of magnetic force

$F=ILB$

$\dfrac{F}{l}=\dfrac{\mu I_{1}I_{2}}{2\pi r}$

Where,

$\dfrac{F}{l}$=force per unit length

I₁= current in first wire

I₂=current in second wire

r = distance between the wires

Put the value into the formula

$88\times10^{4}=\dfrac{4\pi\times10^{-7}\times24\times I_{2}}{2\pi \times7\times10^{-2}}$

$I_{2}=\dfrac{88\times10^{4}\times7\times10^{-2}}{2\times\times10^{-7}\times24}$

$I_{2}=1.3\times10^{10}\ A$

Hence, The current flows in the second wire is $1.3\times10^{10}\ A$