Question

Two long straight parallel wires are separated by 7.0cm. There is a 2.0A current flowing in the first wire. If the magnetic field strength is zero at a distance of 2.2cm from the first wire, then what is the magnitude and diretion of the current in the second wire?

Answer 1

Answer:

The current in the second wire is 4.4 A.

Explanation:

Given that,

Distance =7.0 cm

Current in first wire = 2.0 A

The magnetic field strength is zero at distance of 2.2 cm from the first wire.

We need to calculate the current in the second wire

Using formula of magnetic field

$B=B_{1}-B_{2}$

$0=\dfrac{\mu_{0}I_{1}}{2\pi r_{1}}-\dfrac{\mu_{0}I_{2}}{2\pi r_{2}}$

$\dfrac{\mu_{0}I_{1}}{2\pi r_{1}}=\dfrac{\mu_{0}I_{2}}{2\pi r_{2}}$

$\dfrac{I_{1}}{r_{1}}=\dfrac{I_{2}}{(d-r_{1})}$

Here, $r_{2}=d-r_{1}$

$I_{2}=\dfrac{I_{1}\times(d-r_{1})}{r_{1}}$

Put the value into the formula

$I_{2}=\dfrac{2.0\times(7.0-2.2)}{2.2}$

$I_{2}=4.4\ A$

Hence, The current in the second wire is 4.4 A.