Two concentric circular coils… - JEE Main 2023 Physics PYQ

JEE Main 2023 — Physics Electromagnetism

2023integerhard

Two concentric circular coils with radii $1\mathrm{cm}$ and $1000\mathrm{cm}$ and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____ $\times {10}^{–8}H$ . (Take, ${\pi }^{2}=10$ )

Official previous-year question

Held on 6 Apr 2023 · Verified 6 Jul 2026.

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Solution

Let the magnetic field of the $200$ turns be ${B}_{1}$ . The formula of magnetic field is given by $B=\frac{{\mu }_{0}i}{2r}$

Let $r=1000\mathrm{cm}$ . Thus,

${B}_{1}=\frac{n{\mu }_{0}\times I}{2\times 10}=\frac{200{\mu }_{0}I}{2\times 10}$

The flux through the coil of radius ${r}_{1}=1\mathrm{cm}$ is $\phi =10\times (\vec{B}\cdot \vec{A})$ $=10\times {B}_{1}\pi {{r}^{2}}_{1}$

$\Rightarrow \phi =10\times \frac{200{\mu }_{0}I}{2\times 10}\times \pi {(0.01)}^{2}$

$L=10\times \frac{200{\mu }_{0}}{2\times 10}\times \pi {(0.01)}^{2} =10\times \frac{200(4\pi \times {10}^{-7})}{2\times 10}\times \pi {(0.01)}^{2} =4\times {10}^{-8}H$

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JEE Main 2023 — Physics Electromagnetism

2023integerhard

Official previous-year question

Held on 6 Apr 2023 · Verified 6 Jul 2026.

Did you get this right?

Solution

Let the magnetic field of the $200$ turns be ${B}_{1}$ . The formula of magnetic field is given by $B=\frac{{\mu }_{0}i}{2r}$

Let $r=1000\mathrm{cm}$ . Thus,

${B}_{1}=\frac{n{\mu }_{0}\times I}{2\times 10}=\frac{200{\mu }_{0}I}{2\times 10}$

The flux through the coil of radius ${r}_{1}=1\mathrm{cm}$ is $\phi =10\times (\vec{B}\cdot \vec{A})$ $=10\times {B}_{1}\pi {{r}^{2}}_{1}$

$\Rightarrow \phi =10\times \frac{200{\mu }_{0}I}{2\times 10}\times \pi {(0.01)}^{2}$

$L=10\times \frac{200{\mu }_{0}}{2\times 10}\times \pi {(0.01)}^{2} =10\times \frac{200(4\pi \times {10}^{-7})}{2\times 10}\times \pi {(0.01)}^{2} =4\times {10}^{-8}H$

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Solution

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Solution

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JEE Main Electromagnetism in other years

More JEE Main Electromagnetism questions

Other Physics topics for JEE Main

Mechanics

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Electromagnetism