Question

At what point on the x-axis is the magnetic field zero if the two currents are in the same direction?

Answer 1

0.67cm

Step-by-step explanation:

We are given that

Current ,
`I_1=5A`

`I_2=2.5 A`

`x_1=-2 cm`

`x_2=2 cm`

`d=x_2-x_1=2+2=4 cm`

Let x is the distance between two wires

Magnetic field in the wire,
`B=(2\mu_0I)/(4\pi r)`

Where
`(\mu_0)/(4\pi)=10^(-7)`

`r_1=x`

`r_2=4-x`

`B_1=B_2`

`(2\mu_0 I_1)/(4\pi r_1)=(2\mu_0I_2)/(4\pi r_2)`

`(I_1)/(r_1)=(I_2)/(r_2)`

`(5)/(x)=(2.5)/(4-x)`

`20-5x=2.5x`

`20=2.5x+5x=7.5x`

`x=(20)/(7.5)=2.67 cm`

Distance of 5A wire from the point=-2+2.67=0.67 cm.

Hence, at x=0.67 cm the magnetic field is zero.