Question

Find the magnetic field at the centre of the circular loop shown in the figure.

• A. $\frac{{\mu }_{0}i}{2r}$
• B. $\frac{{\mu }_{0}i\pi }{2r}$
• C. $\frac{{\mu }_{0}i}{2r}\left[\frac{\pi -1}{\pi }\right]$
• D. $\frac{{\mu }_{0}i}{r}$

Answer 1

The correct option is C $\frac{{\mu }_{0}i}{2r}\left[\frac{\pi -1}{\pi }\right]$


Let the magnetic field at point O due to circular loop be$B_1\text{and because of straight current}\text{carrying condutor be}{B}_2{B}_1=\frac{{\mu }_{0}I}{2r}=\frac{{\mu }_{0}i}{2R}{B}_1=\frac{{\mu }_{0}i}{2R}\Rightarrow \text{into the plane}\text{Direction of}{B}_{1}isgivenby:\text{Right hand thumb Rule}{B}_2=\frac{{\mu }_{0}I}{2\pi r}=\frac{{\mu }_{0}i}{2\pi R}\to \text{Out of the plane}\text{Net magnetic field at point O}B=B_1-B_2=\frac{{\mu }_{0}i}{2r}-\frac{{\mu }_{0}i}{2pir}=\frac{{\mu }_{0}i}{2r}[1-\frac{1}{\pi }]B=\frac{{\mu }_{0}i}{2r}\left[\frac{\pi -1}{\pi }\right]$