Question

A very small current carrying circular loop of radius $r$ is placed in $y-z$ plane with centre at origin of coordinate system
The magnetic field at ${\text{P}}_1$ is

• A. $\frac{{\mu }_{0}I{r}^2}{2a^3}\hat{i}$
• B. $\frac{{\mu }_{0}I{r}^2}{4a^3}\hat{j}$
• C. $\frac{{\mu }_{0}I{r}^2}{4a^3}\hat{i}$
• D. $\frac{{\mu }_{0}I{r}^2}{a^3}\hat{i}$

Answer 1

The correct option is A $\frac{{\mu }_{0}I{r}^2}{2a^3}\hat{i}$

From right hand thumb rule we can see that the direction of magnetic field at ${\text{P}}_1$ is along $(+ve)x-$ axis.

Since the circular loop is very small hence the distance of point ${\text{P}}_1$ from its centre is very large. Hence magnetic field at ${\text{P}}_1$ is given by:

$B=\frac{{\mu }_{0}I{r}^2}{2d^3}$

Here $d=a$ and $(a>>r)$

$B=\frac{{\mu }_{0}I{r}^2}{2a^3}$

Using right-hand thumb rule for the direction of field

$\overrightarrow{B}=\frac{{\mu }_{0}I{r}^2}{2a^3}\hat{i}$