Question

A circular loop of radius ' $r$ ' of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field 'B' at its centre. If instead, a circular loop of radius ' $2 r$ ', made of same material, having the same cross section is connected to the same voltage source, what will be the magnetic field at its centre ?
(A) $\frac{B}{2}$
(B) $\frac{B}{4}$
(C) $2 B$
(D) $B$

Answer 1

Ans: (B)
$$\begin{aligned} \text { }: & B=\frac{\mu_{0} I}{2 r}, \quad B^{\prime}=\frac{\mu_{0} I^{\prime}}{2.2 r}, \quad I=\frac{V}{R}, I^{\prime}=\frac{V}{2 R}=\frac{I}{2} \\ B^{\prime} &=\frac{\mu_{0} I^{\prime}}{4 \times 2 r}=\frac{B}{4} \end{aligned}$$

Answer 2

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Answer 3

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