Question 82: Magnetism and Matter

Question

A long conducting wire having a current I flowing through it, is bent into a circular coil of $\mathrm{N}$ turns. Then it is bent into a circular coil of $\mathrm{n}$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is :

Accepted Answer

$I=(2 \pi r) n$
$$
\begin{aligned}
& r \propto\left(\frac{I}{n}ight) \\
& B=n\left(\frac{\mu_{0} i}{2 r}ight) \propto\left(\frac{\mu_{0} i}{2 L}ight) n^{2} \\
& \frac{B_{1}}{B_{2}}=\left(\frac{N^{2}}{n^{2}}ight)
\end{aligned}
$$

Answer

$ N^{2}: n^{2}$

Answer

$\mathrm{N}: \mathrm{n}$

Answer

$\mathrm{n}: \mathrm{N}$

Answer

$n^{2}: N^{2}$

Magnetism and Matter

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