• # question_answer Two circular coils P and Q are made from similar wires but the radius of Q is twice that of P. What should be the value of potential difference across them so that the magnetic field at their centers may be the same? A) ${{V}_{q}}=2{{V}_{p}}$            B) ${{V}_{q}}=3{{V}_{p}}$C) ${{V}_{q}}=4{{V}_{p}}$D)   ${{V}_{q}}=\left( \frac{1}{4} \right){{V}_{p}}$

Correct Answer: C

Solution :

${{B}_{1}}=\frac{{{\mu }_{0}}}{4\pi }\left( \frac{2\pi {{I}_{1}}}{{{r}_{1}}} \right),B=\frac{{{\mu }_{0}}}{4\pi }\left( \frac{2\pi {{I}_{2}}}{{{r}_{2}}} \right)$ ${{r}_{2}}=2{{r}_{1}},{{B}_{1}}={{B}_{2}}$&${{I}_{2}}=2{{I}_{1}}$ $\frac{{{V}_{q}}}{{{V}_{p}}}=\frac{{{I}_{2}}{{r}_{2}}}{{{I}_{1}}{{r}_{1}}}=\frac{2{{I}_{1}}}{{{I}_{1}}}\times \frac{2{{r}_{1}}}{{{r}_{1}}}=\frac{4}{1}$ Hence, the correction option is (c).

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