Question

A current of 1.41 A in a long, straight wire produces a magnetic field of 5.61 uT at a certain distance from the wire. Find

this distance.

Answer 1

0.050 m

Step-by-step explanation:

The strength of the magnetic field produced by a current-carrying wire is given by

`B=(\mu_0 I)/(2\pi r)`

where

`\mu_0=4\pi \cdot 10^(-7) H/m` is the vacuum permeability

I is the current in the wire

r is the distance from the wire

And the magnetic field around the wire forms concentric circles, and it is tangential to the circles.

In this problem, we have:

`I=1.41 A` (current in the wire)

`B=5.61\mu T=5.61\cdot 10^(-6) T` (strength of magnetic field)

Solving for r, we find the distance from the wire:

`r=(\mu_0 I)/(2\pi B)=((4\pi \cdot 10^(-7))(1.41))/(2\pi (5.61\cdot 10^(-6)))=0.050 m`