Electromagnetic Induction PYQs

A rectangular wire loop of sides 8 cm and 3 cm with a small cut, is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the plane of the loop. The emf developed across the cut, if the velocity of the loop is 2 cm s⁻¹, in a direction normal to the shorter side of the loop, will be:

AB is a part of an electrical circuit (see figure). The potential difference $V_A - V_B$, at the instant when current $i = 2\,\text{A}$ and is increasing at a rate of 1 amp / second is:

In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively are through the directions:

The magnetic energy stored in an inductor of inductance 4 μH carrying a current of 2 A is :

The net magnetic flux through any closed surface is :

A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad s⁻¹. If the vertical component of earth's magnetic field at that place is 2 × 10⁻⁵ T and electrical resistance of the coil is 12.56 Ω, then the maximum induced current in the coil will be:

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to a source of potential difference 'V' volts as shown in figure. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10√2 A. The impedance of the circuit is:

Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ >> R₂, the mutual inductance M between them will be directly proportional to:

A circuit when connected to an AC source of 12 V gives a current of 0.2 A. The same circuit when connected to a DC source of 12 V gives a current of 0.4 A. The circuit is:

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 thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from:

The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance:

A long solenoid of diameter $0.1\,\text{m}$ has $2 \times 10^4$ turns per meter. At the centre of the solenoid, a coil of $100$ turns and radius $0.01\,\text{m}$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid decreases uniformly from $4\,\text{A}$ to $0\,\text{A}$ in $0.05\,\text{s}$. If the resistance of the coil is $10\pi^2\,\Omega$, then the total charge flowing through the coil during this time is:

A uniform magnetic field is restricted within a region of radius $r$. The magnetic field changes with time at a rate d$\vec{B}$/dt. Loop 1 of radius $R > r$ encloses the region and loop 2 of radius $R$ is outside the region of magnetic field as shown in the figure below. Then the e.m.f. generated is:

An electron moves on a straight-line path XY as shown. The loop $abcd$ is placed adjacent to the path of the electron. What will be the direction of current, if any, induced in the loop?

A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure. The potential difference developed across the ring when its speed is v, is:

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is

In a coil of resistance 10 Ω, the induced current developed by changing magnetic flux through it is shown in figure as a function of time. The magnitude of change in flux through the coil in Weber is:

A condenser of capacity C is charged to a potential difference of V₁. The plates of the condenser are then connected to an ideal inductor of inductance L. The current through the inductor when the potential difference across the condenser reduces to V₂ is

A conducting circular loop is placed in a uniform magnetic field of $0.04\,T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2\,mm/s$. The induced emf in the loop when the radius is $2\,cm$ is:

A rectangular, a square, a circular and an elliptical loop, all in the $(x-y)$ plane, are moving out of a uniform magnetic field with a constant velocity $\vec{V}=v·\hat{i}$. The magnetic field is directed along the negative $z$-axis direction. The induced emf, during the passage of these loops coming out of the field region, will not remain constant for:

A long solenoid has 500 turns. When a current of 2 ampere is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4 × 10⁻³ Wb. The self-inductance of the solenoid is

A capacitor of capacitance 6 μF is charged by a 6 V battery. It is then connected to an inductor of 5 mH. Find the current in the inductor when one-third of the total energy is magnetic.

Two coils m and n having 10 turns and 15 turns respectively are placed close to each other. When 2 A current is passing through coil m, the flux linked in coil n is 1.8 × 10⁻⁴ Wb per turn. If 3 A current is passed through coil n, calculate the flux linked per turn of coil m.

A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be:

Two coils of self-inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:

As a result of change in the magnetic flux linked to the closed loop shown in the figure, an emf $V$ volt is induced in the loop. The work done (in joules) in taking a charge $Q$ coulomb once along the loop is: