JEE Main 2022 — Physics Electromagnetism

2022integerhard

The displacement current of $4.425\mu A$ is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of ${10}^{6}V{s}^{-1}$ . The area of each plate of the capacitor is $40{\mathrm{cm}}^{2}$ . The distance between each plate of the capacitor is $x\times {10}^{-3}m$ . The value of $x$ is ,

(Permittivity of free space, ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$ ) _______

Official previous-year question

Held on 29 Jun 2022 · Verified 6 Jul 2026.

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Solution

Displacement current is given by ${i}_{d}=$ $\frac{{\epsilon }_{0}d{\phi }_{E}}{dt}$

Or ${i}_{d}=\frac{{\epsilon }_{0}d}{dt}(EA)$ , where $E=\frac{q}{A{\epsilon }_{0}}$

Or ${i}_{d}={\epsilon }_{0}\frac{d}{dt}(\frac{qA}{A{\epsilon }_{0}})=\frac{dq}{dt}=\frac{d}{dt}(CV)$

Or ${i}_{d}=C\frac{dV}{dt}=\frac{{\epsilon }_{0}A}{d}\frac{dV}{dt}$

Putting the values, we have

$4.425\times {10}^{-6}=\frac{8.85\times {10}^{-12}\times 40\times {10}^{-4}\times {10}^{6}}{d}$

$d=2\times {10}^{-6}\times {10}^{-4}\times {10}^{6}\times 40$

$d=80\times {10}^{-4}=8\times {10}^{-3}m$

Hence, value of $x=8$ .

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JEE Main 2022 — Physics Electromagnetism

2022integerhard

(Permittivity of free space, ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$ ) _______

Official previous-year question

Held on 29 Jun 2022 · Verified 6 Jul 2026.

Did you get this right?

Solution

Displacement current is given by ${i}_{d}=$ $\frac{{\epsilon }_{0}d{\phi }_{E}}{dt}$

Or ${i}_{d}=\frac{{\epsilon }_{0}d}{dt}(EA)$ , where $E=\frac{q}{A{\epsilon }_{0}}$

Or ${i}_{d}={\epsilon }_{0}\frac{d}{dt}(\frac{qA}{A{\epsilon }_{0}})=\frac{dq}{dt}=\frac{d}{dt}(CV)$

Or ${i}_{d}=C\frac{dV}{dt}=\frac{{\epsilon }_{0}A}{d}\frac{dV}{dt}$

Putting the values, we have

$4.425\times {10}^{-6}=\frac{8.85\times {10}^{-12}\times 40\times {10}^{-4}\times {10}^{6}}{d}$

$d=2\times {10}^{-6}\times {10}^{-4}\times {10}^{6}\times 40$

$d=80\times {10}^{-4}=8\times {10}^{-3}m$

Hence, value of $x=8$ .

Your note

JEE Main Electromagnetism in other years

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Work through every JEE Main Electromagnetism PYQ, year by year.

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JEE Main 2022 — Physics Electromagnetism

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Solution

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JEE Main 2022 — Physics Electromagnetism

Did you get this right?

Solution

Your note

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