Motional EMF and Eddy Current — JEE Main Physics MCQs with Solutions
Free JEE Main Physics Motional EMF and Eddy Current MCQs with step-by-step solutions (8 questions). Part of Electromagnetic Induction. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Motional EMF and Eddy Current · medium · theory
In which of the following devices, the eddy current effect is not used?
A. Magnetic braking in train
B. Electromagnet
C. Electric heater ✓ Correct
D. Induction furnace
Solution: Electric heaters work on the Joule heating effect of current through a resistor, not on eddy currents. Magnetic braking, electromagnets and induction furnaces all rely on eddy currents induced in bulk conductors by a changing flux.
Q2 — Motional EMF and Eddy Current · medium · theory
A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced emf is
A. once per revolution
B. twice per revolution ✓ Correct
C. four times per revolution
D. six times per revolution
Solution: As the loop rotates, the induced emf varies as $e=e_0\sin\omega t$, which changes sign (direction) twice in every complete revolution — once each time the plane of the loop becomes parallel to $B$.
Q3 — Motional EMF and Eddy Current · medium · numerical
A conductor of length 0.4 m is moving with a speed of 7 m/s perpendicular to a magnetic field of intensity $0.9\text{ Wb/m}^2$. The induced emf across the conductor is
A. $1.26\text{ V}$
B. $2.52\text{ V}$ ✓ Correct
C. $5.04\text{ V}$
D. $25.2\text{ V}$
Solution: $e=Blv\sin\theta$, with $\theta=90^{\circ}$ since $\vec B\perp\vec v$. So $e=0.9\times0.4\times7\times\sin90^{\circ}=2.52\text{ V}$.
Q4 — Motional EMF and Eddy Current · medium · theory
Eddy currents are produced when
A. a metal is kept in a varying magnetic field ✓ Correct
B. a metal is kept in a steady magnetic field
C. a circular coil is placed in a magnetic field
D. current is passed through a circular coil
Solution: Eddy currents are induced currents that circulate within the body of a bulk conductor when the magnetic flux linked with it changes with time, i.e. when the conductor is in a varying (not steady) magnetic field.
Q5 — Motional EMF and Eddy Current · medium · numerical
A conducting square frame of side $a$ and a long straight wire carrying current $I$ are located in the same plane, with the wire running parallel to one side of the frame, passing at a perpendicular distance $x$ from the centre of the frame. The frame moves to the right with a constant velocity $V$. The emf induced in the frame will be proportional to
A. $\dfrac{1}{x^2}$
B. $\dfrac{1}{(2x-a)^2}$
C. $\dfrac{1}{(2x+a)^2}$
D. $\dfrac{1}{(2x-a)(2x+a)}$ ✓ Correct
Solution: The near and far sides of the square frame (at distances $x-\frac{a}{2}$ and $x+\frac{a}{2}$ from the wire) develop motional emfs $e_1=\dfrac{\mu_0IaV}{2\pi(x-a/2)}$ and $e_2=\dfrac{\mu_0IaV}{2\pi(x+a/2)}$, which oppose each other. Net emf $e=e_1-e_2\propto\dfrac{1}{x-a/2}-\dfrac{1}{x+a/2}=\dfrac{a}{x^2-a^2/4}=\dfrac{4a}{(2x-a)(2x+a)}$, so $e\propto\dfrac{1}{(2x-a)(2x+a)}$.
Q6 — Motional EMF and Eddy Current · medium · numerical
A wheel with 20 metallic spokes each 1 m long is rotated with a speed of 120 rpm in a plane perpendicular to a magnetic field of 0.4 G. The induced emf between the axle and rim of the wheel will be ($1\text{ G}=10^{-4}\text{ T}$)
A. $2.51\times10^{-4}\text{ V}$ ✓ Correct
B. $2.51\times10^{-5}\text{ V}$
C. $4.0\times10^{-5}\text{ V}$
D. $2.51\text{ V}$
Solution: All 20 spokes act as identical rotating rods connected in parallel between the axle and rim, so each generates the same emf. $e=\dfrac{1}{2}B(2\pi f)l^2$. Here $B=0.4\text{ G}=0.4\times10^{-4}\text{ T}$, $l=1\text{ m}$, $f=120\text{ rpm}=2\text{ Hz}$. So $e=\dfrac{1}{2}\times0.4\times10^{-4}\times2\pi\times2\times1^2=2.51\times10^{-4}\text{ V}$.
Q7 — Motional EMF and Eddy Current · medium · numerical
A cycle wheel of radius 0.5 m is rotated with constant angular velocity of 10 rad/s in a region of magnetic field of 0.1 T which is perpendicular to the plane of the wheel. The emf generated between its centre and the rim is
A. $0.25\text{ V}$
B. $0.125\text{ V}$ ✓ Correct
C. $0.5\text{ V}$
D. zero
Solution: For a conducting disc/wheel of radius $r$ rotating with angular velocity $\omega$ about its axis, in a field $B$ perpendicular to its plane, $e=\dfrac{1}{2}B\omega r^2=\dfrac{1}{2}\times0.1\times10\times(0.5)^2=0.125\text{ V}$.
Q8 — Motional EMF and Eddy Current · medium · numerical
A thin semicircular conducting ring $PQR$ of radius $r$ is falling with its plane vertical in a horizontal magnetic field $B$ (directed into the plane, with $P$ and $R$ being the ends of the diameter and $Q$ the top of the arc). The potential difference developed across the ring when its speed is $v$ is
A. zero
B. $\dfrac{Bv\pi r^2}{2}$, and $P$ is at higher potential
C. $\pi rBv$, and $R$ is at higher potential
D. $2rBv$, and $R$ is at higher potential ✓ Correct
Solution: The motional emf induced by a curved conductor moving with velocity $v$ perpendicular to $B$ depends only on the effective straight-line length between its endpoints, here the diameter $PR=2r$. So $e=Bv(2r)=2rBv$. Using $\vec F=q\vec v\times\vec B$ on positive charge carriers, electrons are pushed toward $P$, leaving $R$ at the higher potential.