Question

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop $\left(B_L\right)$ to that at the centre of the coil $\left(B_C\right)$, i.e. R $\frac{B_L}{B_C}$ will be

• A. $\frac{1}{N}$
• B. $N^2$
• C. $\frac{1}{N^2}$
• D. $N$

Answer 1

The correct option is C $\frac{1}{N^2}$

$L=2\pi R$ $L=N\times 2\pi r$
$R=Nr$
$B_L=\frac{{\mu }_{0}i}{2R}$ ............(1)

$B_C=\frac{{\mu }_{0}Ni}{2r}$

$B_C=\frac{{\mu }_0{N}^{2}i}{2R}$........(2)

eq${}^n.$ 1 divided by 2.

$\frac{B_L}{B_C}=\frac{1}{N^2}$