JEE Main 2019 — Physics Electromagnetism

2019mcqmedium

Two coils $'P'$ and $'Q'$ are separated by some distance. When a current of $3 A$ flows through coil $'{P}^{'},$ a magnetic flux of ${10}^{-3} Wb$ passes through $'{Q}^{'}.$ No current is passed through $'{Q}^{'}.$ When no current passes through $'P'$ and a current of $2 A$ passes through $'{Q}^{'},$ the flux through $'P'$ is:

Official previous-year question

Held on 9 Apr 2019 · Verified 6 Jul 2026.

Options

A
$3.67\times {10}^{-3} Wb$
B
$6.67\times {10}^{-4} Wb$
C
$3.67\times {10}^{-4} Wb$
D
$6.67\times {10}^{-3} Wb$

Did you get this right?

Solution

Since the coils are co-axial, the flux through the coils can be written as the product of their surface area and the magnetic field produced by the coil along its axis.

Consider the flux passing through Q

${\phi }_{Q}=\frac{{\text{μ}}_{0}{i}_{1}{R}^{2}}{2{({R}^{2}+{x}^{2})}^{\frac{3}{2}}}\times \text{π}{R}^{2}={10}^{-3}\mathrm{Wb}$

And the flux passing through P:

${\phi }_{P}=\frac{{\text{μ}}_{0}{i}_{1}{r}^{2}}{2{({R}^{2}+{x}^{2})}^{\frac{3}{2}}}\times \text{π}{R}^{2}$

Taking the ratio

$\frac{{\phi }_{P}}{{\phi }_{Q}}=\frac{{i}_{2}}{{i}_{1}}\times \frac{{({R}^{2}+{x}^{2})}^{\frac{3}{2}}}{{({R}^{2}+{x}^{2})}^{\frac{3}{2}}}\Rightarrow \frac{{\phi }_{P}}{{10}^{-3}}=\frac{{i}_{2}}{{i}_{1}}$

$\Rightarrow \frac{{\phi }_{P}}{{10}^{-3}}=\frac{2}{3}$

$\therefore {\phi }_{P}=6.67\times {10}^{-4} Wb$

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Solution

Since the coils are co-axial, the flux through the coils can be written as the product of their surface area and the magnetic field produced by the coil along its axis.

Consider the flux passing through Q

${\phi }_{Q}=\frac{{\text{μ}}_{0}{i}_{1}{R}^{2}}{2{({R}^{2}+{x}^{2})}^{\frac{3}{2}}}\times \text{π}{R}^{2}={10}^{-3}\mathrm{Wb}$

And the flux passing through P:

${\phi }_{P}=\frac{{\text{μ}}_{0}{i}_{1}{r}^{2}}{2{({R}^{2}+{x}^{2})}^{\frac{3}{2}}}\times \text{π}{R}^{2}$

Taking the ratio

$\Rightarrow \frac{{\phi }_{P}}{{10}^{-3}}=\frac{2}{3}$

$\therefore {\phi }_{P}=6.67\times {10}^{-4} Wb$

JEE Main 2019 — Physics Electromagnetism

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Solution

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JEE Main 2019 — Physics Electromagnetism

Options

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