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Electromagnetic Induction Set-4 MCQ Online Practice Test | Class 12 | Quiz Tweek

Electromagnetic Induction Set-4

Practice Important MCQs for Electromagnetic Induction — Physics, Class 12.

Electromagnetic induction is one of the most important chapters in Class 12 Physics because it connects changing magnetic fields with induced currents, emf, and electric fields. It forms the foundation for concepts used in generators, transformers, eddy currents, inductors, and many practical electrical devices.

For board exams, this chapter is frequently tested through direct formula-based questions and reasoning problems involving Faraday’s law and Lenz’s law. For JEE and NEET, it is equally important because questions often combine induction with mechanics, energy conservation, and field calculations, making conceptual clarity essential.

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Q1. (A conducting rod of mass $m=0.2\ \mathrm{kg}$ and length $l=0.5\ \mathrm{m}$ slides without friction on two long parallel conducting rails separated by distance $l$ . The rails are connected by a resistor $R=1.0\ \Omega$ , completing the loop. A uniform magnetic field $B=0.5\ \mathrm{T}$ is directed into the plane. At $t=0$ the rod has speed $v_0=1.0\ \mathrm{m\,s^{-1}}$ along the rails and then no external tangential force acts. The total distance $d=\int_0^\infty v\,dt$ the rod travels before coming to rest is:)

(A)

$1.6\ \mathrm{m}$

(B)

$2.0\ \mathrm{m}$

(C)

$3.2\ \mathrm{m}$

(D)

$4.0\ \mathrm{m}$

Q2. (A square conducting loop of side $a$ and resistance $R$ is pulled with constant acceleration across the straight boundary into a region of uniform magnetic field $\mathbf{B}$ (field normal to the plane). While a side is crossing the boundary the magnetic flux through the loop changes. At time $t_1$ the speed of the loop is $v$ and at a later time $t_2$ its speed is $2v$ (still crossing the boundary). The ratios $(\varepsilon_2:\varepsilon_1,\; I_2:I_1,\; P_2:P_1)$ of induced emf, induced current and power dissipated at $t_2$ compared to $t_1$ are:)

(A)

$(2:1,\;2:1,\;4:1)$

(B)

$(4:1,\;2:1,\;16:1)$

(C)

$(1:2,\;1:2,\;1:4)$

(D)

$(2:1,\;4:1,\;8:1)$

Q3. (A conducting rod of length $L$ moves with velocity $\mathbf{v}$ perpendicular to its length through a magnetic field that varies along the rod as $B(x)=B_0\frac{x}{L}$ for $0\le x\le L$ , where $x$ measures position from one end. If $\mathbf{v}\perp\mathbf{B}$ and uniform along the rod, the motional emf between the ends of the rod is:)

(A)

$B_0\,L\,v$

(B)

$\dfrac{2}{3}\,B_0\,L\,v$

(C)

$\dfrac{1}{\sqrt{2}}\,B_0\,L\,v$

(D)

$\dfrac{1}{2}\,B_0\,L\,v$

Q4. (A circular region of radius $a$ contains a magnetic field $B(t)$ uniform inside $r<a$ and zero outside, directed normal to the plane. Using Faraday's law, the magnitude of the induced tangential electric field $E(r)$ at a point with radial distance $r>a$ (outside the magnetic region) is:)

(A)

$\dfrac{r}{2}\left|\dfrac{dB}{dt}\right|$

(B)

$\dfrac{a^{2}}{2r}\left|\dfrac{dB}{dt}\right|$

(C)

$\dfrac{a}{2}\left|\dfrac{dB}{dt}\right|$

(D)

$\dfrac{r^{2}}{2a}\left|\dfrac{dB}{dt}\right|$

Q5. (A rectangular conducting loop consists of two fixed parallel rails and a conducting rod of length $L$ that slides to the right with speed $v$ along the rails, forming a closed rectangle. The region $x>0$ has a magnetic field perpendicular to the plane of the loop with magnitude $B(x)=B_0+\alpha x$ , where $x$ is measured from the boundary at $x=0$ into the field. At an instant the sliding rod is at position $x$ so the area of the portion of the loop inside the field is $Lx$ . The magnitude of the induced emf across the rod at that instant is:

(A)

$L\,v\!\left(B_0+\dfrac{1}{2}\alpha x\right)$

(B)

$L\,v\,(B_0+\alpha x)$

(C)

$L\,v\,B_0$

(D)

$L\,v\!\left(B_0+\dfrac{1}{3}\alpha x\right)$

Q6. (A long solenoid of radius $a$ has $n$ turns per unit length and carries current $I(t)=I_0\cos(\omega t)$ . A circular conducting loop of radius $r$ ( $r>a$ ) is coaxial with the solenoid and lies in the same plane (neglect fringing). The induced electric field at radius $r$ (azimuthal, magnitude) as a function of time is:

(A)

$\dfrac{\mu_0 n a^2 I_0 \omega}{r}\cos(\omega t)$

(B)

$\dfrac{\mu_0 n a^2 I_0 \omega}{2r}\cos(\omega t)$

(C)

$\dfrac{\mu_0 n r^2 I_0 \omega}{2a}\sin(\omega t)$

(D)

$\dfrac{\mu_0 n a^2 I_0 \omega}{2r}\sin(\omega t)$

Q7. (A conducting rod of length $l$ slides without friction on horizontal conducting rails which, together with the rod, form a closed circuit of resistance $R$ . A uniform magnetic field $B$ is into the page. A constant horizontal external force $F$ pulls the rod to the right so that it moves at constant speed $v$ . The required speed $v$ in terms of $F,\;B,\;l,\;R$ is:)

(A)

$v=\dfrac{F\,R}{B^2 l^2}$

(B)

$v=\dfrac{F\,R}{B\,l}$

(C)

$v=\dfrac{F}{B^2 l^2 R}$

(D)

$v=\dfrac{F}{B\,l\,R}$

Q8. (A thin conducting rod of length $L$ rotates with constant angular speed $\omega$ about one fixed end in a plane perpendicular to a magnetic field whose magnitude varies with radial distance as $B(r)=B_0\,(r/L)$ for $0\le r\le L$ . The magnitude of the emf induced between the two ends of the rod is:)

(A)

$\dfrac{1}{2}\,B_0\omega L^2$

(B)

$\dfrac{1}{4}\,B_0\omega L^2$

(C)

$\dfrac{1}{3}\,B_0\omega L^2$

(D)

$\dfrac{2}{3}\,B_0\omega L^2$

Q9. (A rectangular conducting loop of sides $a$ (along the direction of motion) and $l$ (perpendicular to the motion) and resistance $R$ is moved to the right with constant speed $v$ into a region of uniform magnetic field $B$ directed into the page. At an instant when the front edge of the loop is inside the field while the rear edge is still outside, the magnitude of the induced current in the loop is

(A)

$I=\dfrac{B l x}{R}$ , where $x$ is the length of the loop inside the field

(B)

$I=\dfrac{B l v}{R}$

(C)

$I=\dfrac{B a v}{R}$

(D)

$I=0$

Q10. (A conducting rod of length $\ell$ slides without friction on two parallel conducting rails separated by distance $\ell$ ; the rails are connected by a resistor $R$ , forming a closed loop. A constant horizontal force $F$ is applied to the rod and a uniform magnetic field $B$ is directed into the page. In the steady state (constant speed $v$ ), the terminal speed of the rod is

(A)

$v=\dfrac{F}{B\ell}$

(B)

$v=\dfrac{F R}{B\ell}$

(C)

$v=\dfrac{F}{B^2\ell^2 R}$

(D)

$v=\dfrac{F R}{B^2\ell^2}$

Q11. (A coil with $N$ turns and area $A$ rotates in a uniform magnetic field $B$ about an axis perpendicular to the field. It starts from rest at $t=0$ with angular speed $\omega(t)=\alpha t$ (so the rotation angle $\theta(t)=\tfrac{1}{2}\alpha t^2$ ). The induced emf is $\varepsilon(t)=N B A\,\omega(t)\sin\theta(t)$ . The emf becomes zero for the first time after $t=0$ at

(A)

$t=\sqrt{\dfrac{2\pi}{\alpha}}$

(B)

$t=\sqrt{\dfrac{\pi}{\alpha}}$

(C)

$t=\dfrac{2\pi}{\alpha}$

(D)

$t=\sqrt{\dfrac{\pi}{2\alpha}}$

Q12. Inside a long solenoid of radius $R$ the magnetic field is uniform and changing with time: $B(t)$ (axis along the solenoid). Using Faraday's law, the magnitude of the induced electric field $E(r)$ at a distance $r$ from the axis (in the plane perpendicular to the axis) is

(A)

For $r<R$ : $E=\dfrac{R^2}{2r}\left|\dfrac{dB}{dt}\right|$ , for $r>R$ : $E=\dfrac{r}{2}\left|\dfrac{dB}{dt}\right|$

(B)

For both $r<R$ and $r>R$ : $E=\dfrac{r}{2}\left|\dfrac{dB}{dt}\right|$

(C)

For $r<R$ : $E=\dfrac{r}{2}\left|\dfrac{dB}{dt}\right|$ , for $r>R$ : $E=\dfrac{R^2}{2r}\left|\dfrac{dB}{dt}\right|$

(D)

$E=0$ because there is no conducting circuit present

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