CBSE 2024 · Region 1 · Set 3 · Q24 · 3 marks
A circular coil with cross-sectional area $\displaystyle 0.2 \mathrm{~cm}^2$ carries a current of $\displaystyle 4$ A. It is kept in a uniform magnetic field of magnitude $\displaystyle 0.5$ T normal to the plane of the coil. Calculate:(a)the net force on the coil.(b)the torque on the coil.(c)the average force on each electron in the coil due to the magnetic field. The free electron density in the material of the coil is $\displaystyle 10^{28} \mathrm{~m}^{-3}$.
A circular coil with cross-sectional area $\displaystyle 0.2 \mathrm{~cm}^2$ carries a current of $\displaystyle 4$ A. It is kept in a uniform magnetic field of magnitude $\displaystyle 0.5$ T normal to the plane of the coil. Calculate:
(a)
the net force on the coil.
(b)
the torque on the coil.
(c)
the average force on each electron in the coil due to the magnetic field. The free electron density in the material of the coil is $\displaystyle 10^{28} \mathrm{~m}^{-3}$.
Marking-scheme solution
Calculating
(a) Net force = zero By symmetry, force on each element of the coil is equal and opposite to the force on the diametrically opposite element of the coil. Hence, the net force is zero.
Alternatively :
\[\begin{aligned}
& d \vec{f}_{1}=I \overrightarrow{d l} \times \vec{B} \\
& d \vec{f}_{2}=I \overrightarrow{d l} \times \vec{B} \\
& \vec{F}_{1}=-\vec{F}_{2}
\end{aligned}
\]
On coil magnetic force are equal
and opposite, so they will cancel out each other.
and opposite, so they will cancel out each other.(b) Torque on the coil.
\[\begin{aligned}
& \vec{\tau}=\vec{m} \times \vec{B} \\
& \tau=m B \sin \theta \quad[\vec{m} \| \vec{B}] \\
& \tau=m B \sin 0^{\circ} \quad \theta=0^{\circ} \\
& \tau=0
\end{aligned}
\]
(c) \[\begin{aligned}
f_{\text {avg }} & =e\left(\overrightarrow{\mathrm{v}}_{d} \times \vec{B}\right) \\
& =e \mathrm{v}_{d} B \sin 90^{\circ} \\
& =e \mathrm{v}_{d} B
\end{aligned}
\]
\[\therefore I=n e A \mathrm{v}_{d}
\]
Moving Charges and MagnetismTorque on Current Loop, Magnetic DipoleApplyshort_answermedium
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CBSE Class 12 Physics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.