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Magnetic Field Due to Current Carrying Circular Loop

Two semicircl...

Question

Two semicircles are shown in the figure having radius $R_{1}$ and $R_{2}$ , carrying current $I_{1}$ and $I_{2}$ respectively. Find the ratio $\frac{I_{1}}{I_{2}}$ so that the net magnetic field at the centre is zero.
(Assume that straight wire segments pass through the centre.)

A

\frac{R_{1}}{R_{2}}

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B

\sqrt{\frac{R_{1}}{R_{2}}}

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C

{(\frac{R_{1}}{R_{2}})}^{3}

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D

{(\frac{R_{1}}{R_{2}})}^{2}

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Solution

The correct option is A $\frac{R_{1}}{R_{2}}$

We know that, magnetic field due to a semi-circular loop at the centre is given by,

$B_{O} = \frac{μ_{o} I}{4 r}$

As the net magnetic field at the centre is zero, so,

$\frac{μ_{o} I_{1}}{4 R_{1}} = \frac{μ_{o} I_{2}}{4 R_{2}}$

$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{R_{1}}{R_{2}}$

Why this question?
The magnetic field due to a semi-circular loop at the centre is given by, $B = \frac{μ_{o} I}{4 a}$ .

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Magnetic Field Due to Current Carrying Circular Loop

Standard X Physics

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