Multiple Choice & Assertion-Reason

PHYExam Practice

This is a chapter-wide revision article for the one-mark MCQs and Assertion-Reason items that sweep across all of magnetism: fields from currents, the magnetic force $\vec{F} = q\vec{v}\times\vec{B}$ , cyclotron motion, dipole torque and energy, meter conversions, and the Earth's field. These questions reward instant recall of the standard SI formulas and the qualitative behaviour (parallel velocity gives zero force, parallel wires with same-direction currents attract, etc.).

The Assertion-Reason items typically probe galvanometer sensitivity and the dip-angle limits, where one clean relation settles the answer.

Field at centre of a circular coil (

N

turns)

B = \dfrac{\mu_0 N I}{2R}

\mu_0 = 4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}

I

current,

R

radius,

N

number of turns (a single turn gives

\mu_0 I/2R

Lorentz magnetic force

\vec{F} = q\,\vec{v}\times\vec{B}, \qquad F = qvB\sin\theta

\theta

is the angle between

\vec{v}

and

\vec{B}

;

F=0

when

\theta=0^{\circ}

(parallel) and maximum when

\theta=90^{\circ}

Cyclotron frequency

f = \dfrac{qB}{2\pi m}

Independent of speed and radius; depends only on the charge-to-mass ratio

q/m

and the field

B

Torque and energy of a magnetic dipole

\tau = mB\sin\theta, \qquad U = -mB\cos\theta

m

dipole moment,

\theta

angle between

\vec{m}

and

\vec{B}

;

U

is minimum (

-mB

) when

\vec{m}\parallel\vec{B}

Galvanometer sensitivities

S_I = \dfrac{\theta}{I} = \dfrac{NBA}{k}, \qquad S_V = \dfrac{S_I}{G}

S_I

current sensitivity,

S_V

voltage sensitivity,

G

coil resistance,

k

torsion constant,

N,B,A

turns/field/area.

SI unit of magnetic dipole moment is $\mathrm{A\,m^2}$ (equivalently $\mathrm{J\,T^{-1}}$ ); SI unit of $B$ is the tesla $\mathrm{T} = \mathrm{Wb\,m^{-2}}$ .
A charge moving parallel ( $\theta=0^{\circ}$ ) or antiparallel ( $\theta=180^{\circ}$ ) to $\vec{B}$ feels zero force; the magnetic force never does work, so speed and kinetic energy stay constant.
Ammeter: low-resistance shunt $S$ in parallel. Voltmeter: high resistance $R$ in series. Mnemonic: an ammeter carries the large line current, so it must have tiny resistance.
Two long parallel wires attract if their currents are in the same direction and repel if opposite.
Inside a long solenoid the field is uniform and directed along the axis, $B=\mu_0 nI$ ; outside it is nearly zero.
Dipole potential energy: minimum ( $-mB$ ) when $\vec{m}\parallel\vec{B}$ (stable), zero at $\theta=90^{\circ}$ , maximum ( $+mB$ ) when antiparallel (unstable).
Angle of dip is $0^{\circ}$ at the magnetic equator and $90^{\circ}$ at the magnetic poles.
Increasing turns $N$ raises current sensitivity $S_I=NBA/k$ , but also raises coil resistance $G$ , so voltage sensitivity $S_V=S_I/G$ need not increase — this is the key to the standard A-R item.

Where the marks go

Mixing up $\mu_0 I/2R$ (centre of a loop) with $\mu_0 I/2\pi R$ (long straight wire) — the $\pi$ only appears for the straight wire.
Stating that current sensitivity and voltage sensitivity always rise together; they do not, because $S_V = S_I/G$ and $G$ grows with $N$ .
Writing the dipole energy minimum as the perpendicular orientation; it is minimum when $\vec{m}$ is parallel to $\vec{B}$ .
Confusing the ammeter (shunt in parallel) with the voltmeter (high resistance in series).

How the board asks it

Assertion–Reasonvoltage vs current sensitivity
Assertion (A): Increasing the number of turns $N$ in a moving-coil galvanometer always increases its voltage sensitivity. Reason (R): Current sensitivity is given by $S_I=NBA/k$ , which rises with $N$ . Choose: (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.
Assertion–Reasonmagnetic force does no work
Assertion (A): A charged particle that enters a uniform magnetic field moves with constant speed. Reason (R): The magnetic force $\vec{F}=q\vec{v}\times\vec{B}$ is always perpendicular to the velocity and so does no work on the particle. Choose: (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.
Assertion–Reasonangle of dip limits
Assertion (A): At the magnetic equator the angle of dip is $0^{\circ}$ . Reason (R): At the magnetic poles a freely suspended dip needle rests horizontal. Choose: (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.
Numericalfield at centre of a circular coil
A circular coil of $50$ turns and radius $5\,\mathrm{cm}$ carries a current of $2\,\mathrm{A}$ . Calculate the magnitude of the magnetic field at its centre. $(\mu_0=4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}})$
Applicationforce between parallel currents
Two long straight parallel wires carry currents in the same direction. State, with reason, whether the force between them is attractive or repulsive.
Define / stateSI unit of magnetic dipole moment
State the SI unit of magnetic dipole moment and give one equivalent form of this unit.

PreviousTerrestrial Magnetism (Earth's Field)

Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.