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

The current in the second wire is 4.4 A.

Step-by-step 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=(\mu_(0)I_(1))/(2\pi r_(1))-(\mu_(0)I_(2))/(2\pi r_(2))`

`(\mu_(0)I_(1))/(2\pi r_(1))=(\mu_(0)I_(2))/(2\pi r_(2))`

`(I_(1))/(r_(1))=(I_(2))/((d-r_(1)))`

Here,
`r_(2)=d-r_(1)`

`I_(2)=(I_(1)*(d-r_(1)))/(r_(1))`

Put the value into the formula

`I_(2)=(2.0*(7.0-2.2))/(2.2)`

`I_(2)=4.4\ A`

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