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Moving Charges and Magnetism Set-3

Practice Important MCQs for Moving Charges and Magnetism — Physics, Class 12.

This chapter forms the backbone of many board- and competition-level problems: it links kinematics of charged particles with magnetic-field sources (wires, loops, solenoids) and introduces key laws (Lorentz force, Biot–Savart, Ampère–Maxwell) that appear repeatedly in JEE/NEET-style multi-step questions. Mastery helps solve beam-deflection devices, cyclotron/velocity-filter problems, magnetic field distributions and force/torque questions on current loops — all high-yield for both theory and numericals.

Beyond routine formula use, questions in this topic often require synthesis — choosing the right integral form, recognising when induced electric fields appear, or deciding whether a non-uniform field produces net force or only torque. Practising varied data/graph interpretation and assertion–reason reasoning here builds the problem-solving agility needed for CBSE board papers and competitive exams.

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Q1. An electron (mass $m_e=9.11\times10^{-31}\ \text{kg}$ , charge $e=1.60\times10^{-19}\ \text{C}$ ) moves perpendicular to a uniform magnetic field $B=5.0\times10^{-4}\ \text{T}$ with speed $v=2.0\times10^{6}\ \text{m/s}$ . The radius $r$ of its circular trajectory is

(A)

$1.14\times10^{-2}\ \text{m}$

(B)

$4.55\times10^{-2}\ \text{m}$

(C)

$2.28\times10^{-2}\ \text{m}$

(D)

$9.11\times10^{-3}\ \text{m}$

Q2. A coil has $N=50$ turns. The magnetic flux through each turn varies with time as $\Phi(t)=2.0\times10^{-3}\,t-5.0\times10^{-4}\,t^{2}$ Wb for $0\le t\le4\ \text{s}$ . The magnitude of the induced emf in the coil at $t=2.0\ \text{s}$ is

(A)

$0\ \text{V}$

(B)

$1.0\times10^{-1}\ \text{V}$

(C)

$2.0\times10^{-2}\ \text{V}$

(D)

$5.0\times10^{-2}\ \text{V}$

Q3. Electrons are accelerated from rest through a potential difference $V=150\ \text{V}$ and enter a region with perpendicular electric field $E=5.0\times10^{4}\ \text{V/m}$ and a magnetic field $B$ (both fields perpendicular to the electron velocity and to each other). What magnitude of $B$ is required so that electrons pass undeflected through the region?

(A)

$1.45\times10^{-3}\ \text{T}$

(B)

$3.44\times10^{-2}\ \text{T}$

(C)

$1.38\times10^{-2}\ \text{T}$

(D)

$6.88\times10^{-3}\ \text{T}$

Q4. A very long cylindrical conductor of radius $R$ carries steady total current $I$ . A measured plot of magnetic field magnitude $B$ versus radial distance $r$ from the axis shows $B\propto r$ for $r<R$ and $B\propto 1/r$ for $r>R$ . Which current distribution inside the conductor is consistent with this plot?

(A)

$J(r)\propto r$ (current density proportional to distance from axis)

(B)

$J(r)=\text{constant}$ (uniform current density)

(C)

All current flows as a thin layer at $r=R$ (surface current)

(D)

$J(r)\propto 1/r$ (singular at axis)

Q5. A long solid cylindrical conductor of radius $R$ carries total current $I$ . The volume current density varies as $J(r)=k\,r$ (proportional to radial distance $r$ from axis). Using Ampère's law, the magnetic field at a distance $r$ inside the conductor is $B(r)=\dfrac{\mu_{0}I}{2\pi R^{3}}\,r^{2}$ . The magnitude of $B$ at $r=\dfrac{R}{2}$ equals

(A)

$\dfrac{\mu_{0}I}{4\pi R}$

(B)

$\dfrac{\mu_{0}I}{16\pi R}$

(C)

$\dfrac{\mu_{0}I}{8\pi R}$

(D)

$\dfrac{\mu_{0}I}{2\pi R}$

Q6. Assertion (A): Ampère's circuital law written as $\displaystyle\oint_{C}\vec{B}\cdot d\vec{\ell}=\mu_{0}I_{\text{enc}}$ is valid without modification for any time-dependent current distribution.
Reason (R): To make Ampère's law valid for time-varying situations one must add the displacement current term $\mu_{0}\varepsilon_{0}\dfrac{d\Phi_{E}}{dt}$ ; the general form is $\displaystyle\oint_{C}\vec{B}\cdot d\vec{\ell}=\mu_{0}\bigl(I_{\text{enc}}+\varepsilon_{0}\dfrac{d\Phi_{E}}{dt}\bigr)$ .

(A)

Both A and R are true and R is the correct explanation of A.

(B)

Both A and R are true but R is not the correct explanation of A.

(C)

A is true but R is false.

(D)

A is false but R is true.

Q7. A spatially uniform magnetic field $\vec{B}(t)=B_{0}+\alpha t$ (directed along $+\hat{z}$ ) increases linearly with time. A positive ion initially at rest at the origin will

(A)

remain at rest because a purely magnetic field cannot exert a force on a stationary charge

(B)

be set into motion because the time-varying magnetic field induces a non-conservative electric field that does work on the ion

(C)

start moving in a circle about the $z$ -axis due to $q\vec{v}\times\vec{B}$ and thereby increase its speed

(D)

remain at rest unless there is an external applied electric field (no induced fields are present if $B$ is spatially uniform)

Q8. A thin wire carries current $I=5.0\ \text{A}$ and is bent into a semicircle of radius $R=0.10\ \text{m}$ whose ends are joined to two semi-infinite straight wires that extend radially outward from the ends of the semicircle to infinity. The magnitude of the net magnetic field at the centre of the semicircle (due to the entire wire) is

(A)

$2.57\times10^{-5}\ \text{T}$

(B)

$1.57\times10^{-5}\ \text{T}$

(C)

$3.14\times10^{-5}\ \text{T}$

(D)

$2.00\times10^{-5}\ \text{T}$

Q9. Assertion (A): A charged particle moving in a region where the magnetic field is spatially non-uniform but time-independent can have its speed increased purely by the magnetic force.
Reason (R): The magnetic part of the Lorentz force is $q\vec{v}\times\vec{B}$ which is always perpendicular to $\vec{v}$ , so it does no work and cannot change the particle's kinetic energy.

(A)

Both A and R are true and R is the correct explanation of A.

(B)

Both A and R are true but R is not the correct explanation of A.

(C)

A is true but R is false.

(D)

A is false but R is true.

Q10. A small circular loop (area $A=2.0\times10^{-4}\ \text{m}^2$ ) carries current $I=1.0\ \text{A}$ . Its magnetic moment $\vec{\mu}$ points along $+\hat{x}$ . The loop sits near $x=0$ in a magnetic field $\vec{B}(x)=0.2\,(1+50x)\,\hat{x}$ (tesla, with $x$ in metres). Treating the loop as a magnetic dipole, the net force on the loop is approximately

(A)

$\vec{F}=\vec{0}$

(B)

$2.0\times10^{-3}\ \text{N}$ in the $+x$ direction

(C)

$4.0\times10^{-3}\ \text{N}$ in the $+x$ direction

(D)

a pure torque only; no net translational force acts on the loop

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