Question

The magnetic field at a distance $\mathrm{r}$ from a long wire carrying current i is $0.4\mathrm{T}$. the magnetic field at a distance of $2\mathrm{r}$ is

Answer 1

Step 1: Magnetic field

The magnetic field along a current-carrying long straight wire of length r is given as: $\mathrm{B}=\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{\pi r}}$, where ${\mathrm{\mu }}_0$ is magnetic permeability of free space; $\mathrm{i}$ is the current in the wire; $\mathrm{r}$ is the distance of a point from the wire.

Step 2: Explanation

When the length is $\mathrm{r}$ the magnetic field $\mathrm{B}$ is $0.4\mathrm{T}$

When length becomes $2\mathrm{r}$ then,

$$\begin{gathered} \Rightarrow {\mathrm{B}}^{\text{'}}=\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{\pi }\left(2\mathrm{r}\right)} \\ \Rightarrow {\mathrm{B}}^{\text{'}}=\frac{1}{2}\times \frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{\pi r}} \\ \Rightarrow {\mathrm{B}}^{\text{'}}=\frac{1}{2}\times 0.4=0.2\mathrm{T} \end{gathered}$$

Hence, when the length of the wire is doubled the Magnetic field is reduced by half.