Question

How would the strength of magnetic field due to current-carrying loop be affected if strength of current through the loop is doubled?

Answer 1

Step1: Expression for the magnetic field due to the current carrying loop

The magnetic field due to the current carrying loop is given as:

$B=\frac{{\mu }_{o}i}{2R}$………. (1)

Here ${\mu }_o$ is the permeability of free space, i is the current, R is the radius

Step2: Expression for the magnetic field when strength of the current is doubled

If the current through the loop is doubled then: $i=2i$

Using the equation(1):

$$\begin{gathered} B\text{'}=\frac{{\mu }_{o}i}{2R}=\frac{{\mu }_o\left(2i\right)}{2R} \\ B\text{'}=2\left(\frac{{\mu }_{o}i}{2R}\right) \\ B\text{'}=2B \end{gathered}$$

Step3: Conclusion from the above expression

Therefore, the strength of the magnetic field due to current-carrying loop is doubled when the current through the loop is doubled.