Question

An experiment on the earth's magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current int eh cable if the experiment is to be accurate?

Answer 1

Answer:

The allowed current in the cable is 1.15 A.

Explanation:

Given that,

Distance = 1.00 m

Suppose the magnetic field is $2.3\times10^{-5}\ T$ and  if the experiment is to be accurate to 1.0 %

We need to calculate the current

Using formula of magnetic field

$B=\dfrac{\mu_{0}I}{2\pi r}$

$I=\dfrac{B\times2\pi r}{\mu_{0}}$

Put the value into the formula

$I=\dfrac{2.3\times10^{-5}\times2\times\pi\times1.00}{4\pi\times10^{-7}}$

$I=115\ A$

If the experiment is to be accurate to 1.0%

Then,

We need to calculate the allowed current in the cable

$I'=(1.0%)\times I$

$I'=\dfrac{1.0}{100}\times115$

$I'=1.15\ A$

Hence, The allowed current in the cable is 1.15 A.