JEE Main 2019 — Physics Electromagnetism

2019mcqmedium

A conducting circular loop made of a thin wire has area $3.5\times {10}^{-2} {m}^{2}$ and resistance $10 \Omega$ It is placed perpendicular to a time-dependent magnetic field $B(t)=(0.4T)\mathrm{sin}⁡(50\pi t)$ The field is uniform in space. Then the net charge flowing through the loop during $t=0 s$ and $t=10 \mathrm{ms}$ is close to

Official previous-year question

Held on 9 Jan 2019 · Verified 6 Jul 2026.

Options

A
$1.4 mC$
B
$7 mC$
C
$21 mC$
D
$6 mC$

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Solution

It is given that, the magnetic field,

$B=0.4 sin(50\pi t)$

and the area of the given circular conducting loop,

$A=3.5\times {10}^{-2}{m}^{2}$

Magnetic flux,

$\phi =BA...(1)$

Then, induced emf,

$\epsilon =|\frac{d\phi }{dt}|...(2)$

When resistance in the circuit is $R$ , the differential charge accumulated, based on current $i$ ,

$dQ=idt=\frac{\epsilon }{R}dt=\frac{1}{R}d\phi \Rightarrow \Delta Q=\frac{1}{R} \int d\phi =\frac{1}{R} \Delta \phi$

Substituting given values and using equation $(1)$ and $(2)$ ,

$\Delta Q=\frac{1}{10}[0.4\mathrm{sin}(50\pi \times 10\times {10}^{-3})-0]\times 3.5\times {10}^{-2} \Rightarrow \Delta Q=\frac{0.4\times 3.5\times {10}^{-2}}{10}=1.4\times {10}^{-3}C$

$\Rightarrow \Delta Q=1.4\mathrm{mC}$

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Solution

It is given that, the magnetic field,

$B=0.4 sin(50\pi t)$

and the area of the given circular conducting loop,

$A=3.5\times {10}^{-2}{m}^{2}$

Magnetic flux,

$\phi =BA...(1)$

Then, induced emf,

$\epsilon =|\frac{d\phi }{dt}|...(2)$

When resistance in the circuit is $R$ , the differential charge accumulated, based on current $i$ ,

$dQ=idt=\frac{\epsilon }{R}dt=\frac{1}{R}d\phi \Rightarrow \Delta Q=\frac{1}{R} \int d\phi =\frac{1}{R} \Delta \phi$

Substituting given values and using equation $(1)$ and $(2)$ ,

$\Delta Q=\frac{1}{10}[0.4\mathrm{sin}(50\pi \times 10\times {10}^{-3})-0]\times 3.5\times {10}^{-2} \Rightarrow \Delta Q=\frac{0.4\times 3.5\times {10}^{-2}}{10}=1.4\times {10}^{-3}C$

$\Rightarrow \Delta Q=1.4\mathrm{mC}$

JEE Main 2019 — Physics Electromagnetism

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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