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Magnetic Field Due to Current in a Solenoid

Two concentri...

Question

Two concentric circular loops of radii $r_{1}$ and $r_{2}$ carry clockwise and anticlockwise currents $i_{1}$ and $i_{2}$ . If the the centre is a null point, then $i_{1}$ / $i_{2}$ ?

r_{2} / r_{1}

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r_{2}^{2} / r_{1}^{2}

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r_{1}^{2} / r_{2}^{2}

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r_{1} / r_{2}

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Solution

The correct option is D $r_{1} / r_{2}$
B at centre $\frac{μ_{o} i}{2 r},$ for zero magnetic field at centre,
$∴$ field produced by inner ring should be equal and opposite to that of ring 2.
$\frac{μ_{o} I_{1}}{2 r_{1}} = \frac{μ_{o} I_{2}}{2 r_{2}}$
$\frac{i_{1}}{i_{2}} = \frac{r_{1}}{r_{2}}$

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If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

If the sum of the areas of two circles with radii $R_{1}$ and $R_{2}$ is equal to the area of a circle of radius R then

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