Physics - Magnetism Question with Solution | TestHub

The wire of length $l$ is bent to from a circular loop, so $2\pi r=l$ $$\Rightarrow r=\frac{l}{2\pi }$$ The magnetic field at the centre of the loop is $$B=\frac{{\mu }_{0}I}{2r}=\frac{{\mu }_{0}I\times 2\pi }{2l}$$ Now the same length of the wire is bent to from a double loop $$\begin{array}{rl}& \therefore 2\times 2\pi r^{\prime }=l\\ & \Rightarrow r^{\prime }=\frac{l}{4\pi }\end{array}$$ And the magnetic field at the centre $$\begin{array}{rl}& B^{\prime }=\frac{{\mu }_{0}I\times 2}{2\times r^{\prime }}=\frac{2{\mu }_{0}I}{2\times \frac{l}{4\pi }}=\frac{2\times 4\pi \mu I}{2l}\\ & \therefore \frac{B^{\prime }}{B}=4\Rightarrow B^{\prime }=4B\end{array}$$