JEE Electromagnetic Induction PYQs with Solutions PDF

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. lf the resistance of the total circuit is 2Ω then the force needed to move the rod towards right with constant speed (v) of 1.5 m/s is ___ N

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $$30 ^{\circ}$$ from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is ____ mm. (Take $$\pi = \frac{22}{7}$$)

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity $$(g=10m/s^{2})$$ through a uniform horizontal magnetic fie ld of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travells a vertical distance of200 m is ____ mV.

Three identical coils $$C_{1}, C_{2}$$ and $$C_{3}$$ are closely placed such that they share a common axis. $$C_{2}$$ is exactly midway. $$C_{1}$$ carries current $$I$$ in anti-clockwise direction while $$C_{3}$$ carries current $$I$$ in clockwise direction. An induced Current flows through $$C_{2}$$ will be in clockwise direction when

$$XPQY$$ is a vertical smooth long loop having a total resistance $$R$$ where $$PX$$ is parallel to $$QY$$ and separation between them is $$l$$. A constant magnetic field $$B$$ perpendicular to the plane of the loop exists in the entire space. A rod $$CD$$ of length $$L (L > l)$$ and mass $$m$$ is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is _______ $$m/s. (g$$ = acceleration due to gravity)

Inductance of a coil with $$ 10^{4} $$ tums is $$10 mH$$ and it is connected to a dc source of $$10 V$$ with internal resistance of $$10\Omega $$ The energy density in the inductor when the
current reaches $$ \left( \frac{1}{e} \right) $$ of its maximum value is $$ \alpha\pi \times \frac{1}{e^{2}}J/m^{3} $$. The value of $$ \alpha$$ is_______.
$$ (\mu_{o}=4\pi\times 10^{-7}Tm/A). $$

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $$I= 10 \sin (\omega t)$$ A, where $$\omega$$ = 1000 rad.ls. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed $$v = 1 cm/s$$. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is $$\alpha/\sqrt{2}\mu A$$. The value of $$\alpha$$ is ______.
[Resistance of the loop= 10$$\Omega$$]

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf (ε) with time (t) is given by

A coil of area A and N turns is rotating with angular velocity $$\omega$$ in a uniform magnetic field $$\overrightarrow{B}$$ about an axis perpendicular to $$\overrightarrow{B}$$. Magnetic flux $$\varphi$$ and induced emf ε across it, at an instant when $$\overrightarrow{B}$$ is parallel to the plane of coil, are :

Regarding self-inductance:
A. The self-inductance of the coil depends on its geometry.
B. Self-inductance does not depend on the permeability of the medium.
C. Self-induced e.m.f. opposes any change in the current in a circuit.
D. Self-inductance is electromagnetic analogue of mass in mechanics.
E. Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A/s. At an instant when R is $$12\Omega$$ , the value of the current in the circuit will be ______ A.

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of $$10\pi rads^{-1}$$ about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim ? $$(\pi = 3.14)$$

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time $$t = 0$$ with a constant velocity. If the induced EMF is $$E \propto t^n$$. then value of n is _.

A rectangular loop of sides $$12$$ cm and $$5$$ cm, with its sides parallel to the $$x$$-axis and $$y$$-axis respectively moves with a velocity of $$5$$ cm s$$^{-1}$$ in the positive $$x$$ axis direction, in a space containing a variable magnetic field in the positive $$z$$ direction. The field has a gradient of $$10^{-3}$$ T cm$$^{-1}$$ along the negative $$x$$ direction and it is decreasing with time at the rate of $$10^{-3}$$ T s$$^{-1}$$. If the resistance of the loop is $$6$$ m$$\Omega$$, the power dissipated by the loop as heat is ______ $$\times 10^{-9}$$ W.

A rectangular loop of length $$2.5$$ m and width $$2$$ m is placed at $$60°$$ to a magnetic field of $$4$$ T. The loop is removed from the field in $$10$$ sec. The average emf induced in the loop during this time is

Two coils have mutual inductance $$0.002$$ H. The current changes in the first coil according to the relation $$i = i_0 \sin \omega t$$, where $$i_0 = 5$$ A and $$\omega = 50\pi \text{ rad s}^{-1}$$. The maximum value of emf in the second coil is $$\frac{\pi}{\alpha}$$ V. The value of $$\alpha$$ is

The electric potential at the surface of an atomic nucleus ($$Z = 50$$) of radius $$9 \times 10^{-13}$$ cm is $$\alpha \times 10^6$$ V. What is the value of $$\alpha$$?
(Charge of proton $$1.6 \times 10^{-19}$$ C)

A horizontal straight wire $$5$$ m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field $$0.60 \times 10^{-4}$$ Wb m$$^{-2}$$. The instantaneous value of emf induced in the wire when its velocity is $$10 \text{ m s}^{-1}$$ is ______ $$\times 10^{-3}$$ V.

A ceiling fan having $$3$$ blades of length $$80 \text{ cm}$$ each is rotating with an angular velocity of $$1200 \text{ rpm}$$. The magnetic field of earth in that region is $$0.5 \text{ G}$$ and angle of dip is $$30°$$. The emf induced across the blades is $$N\pi \times 10^{-5} \text{ V}$$. The value of $$N$$ is ______.

A coil is placed perpendicular to a magnetic field of $$5000$$ T. When the field is changed to $$3000$$ T in $$2$$ s, an induced emf of $$22$$ V is produced in the coil. If the diameter of the coil is $$0.02$$ m, then the number of turns in the coil is:

A small square loop of wire of side $$l$$ is placed inside a large square loop of wire of side $$L(L = l^2)$$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $$\sqrt{x} \times 10^{-7}$$ H, where $$x$$ = ______.

The magnetic flux $$\phi$$ (in weber) linked with a closed circuit of resistance 8 $$\Omega$$ varies with time (in seconds) as $$\phi = 5t^2 - 36t + 1$$. The induced current in the circuit at $$t = 2$$ s is ______ A.

A rod of length $$60$$ cm rotates with a uniform angular velocity $$20$$ rad s$$^{-1}$$ about its perpendicular bisector, in a uniform magnetic field $$0.5$$ T. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _____ V.

The current in an inductor is given by $$I = (3t + 8)$$ where $$t$$ is in second. The magnitude of induced emf produced in the inductor is $$12$$ mV. The self-inductance of the inductor ______ mH.

In a coil, the current changes from $$-2 \text{ A}$$ to $$+2 \text{ A}$$ in $$0.2 \text{ s}$$ and induces an emf of $$0.1 \text{ V}$$. The self inductance of the coil is :

An electric field, $$\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$$ passes through the surface of $$4 \text{ m}^2$$ area having unit vector $$\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$$. The electric flux for that surface is ______ Vm.

Match the List-I with List-II:

Choose the correct answer from the options given below:

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed:
A. By changing the magnitude of the magnetic field within the coil.
B. By changing the area of coil within the magnetic field.
C. By changing the angle between the direction of magnetic field and the plane of the coil.
D. By reversing the magnetic field direction abruptly without changing its magnitude.
Choose the most appropriate answer from the options given below:

A square shaped coil of area $$70 \text{ cm}^2$$ having 600 turns rotates in a magnetic field of $$0.4 \text{ Wb m}^{-2}$$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $$60°$$ with the field, will be ______ V.
(Take $$\pi = \frac{22}{7}$$)

A conducting loop of radius $$\frac{10}{\sqrt{\pi}}$$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is: