The magnetic field at the centre \(\mathrm{C}\) of the arrangement shown in figure is
The magnetic field at the centre \(\mathrm{C}\) of the arrangement shown in figure is
\(\frac{\mu_0 i}{2 \pi r}(1+\pi)\)
\(\frac{\mu_0 i}{4 \pi r}(1+\pi)\)
\(\frac{\mu_0 i}{\pi r}(1+\pi)\)
\(\frac{\mu_0 i}{r}(1+\pi)\)
Solution
According to diagram in the question, magnetic field at the centre \(C\) will be sum of the magnetic field due to straight part \(B_1\) and magnetic field due to circular part \(B_2\).
\(\because\) From Maxwell's right hand thumb rule direction of both magnetic field at the point \(C\) will be same and above the plane of paper.
So, \(B_C=B_1+B_2=\frac{\mu_0 i}{4 \pi r}+\frac{\mu_0 i}{4 r}=\frac{\mu_0 i}{4 \pi r}(1+\pi)\)
Hence, the magnetic field at the centre \(C\) of the arrangement shown in figure is, \(\frac{\mu_0}{4 \pi r} i(1+\pi)\).
