Other: Induction & Displacement Current

A square of side ' $L$ ' metre lies in $x-y$ plane in a region where the magnetic field is$\vec{B}$and $\vec{B} = B_0(2\hat{i} + 3\hat{j} + 4\hat{k})$, where $B_0$ is constant. The magnitude of flux passing through the square (in weber) is

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is:

A boat is moving due east in a region where the earth's magnetic field is $3.6 \times 10^{-5}\text{ N/Am}$ due north and horizontal. The boat carries a vertical conducting rod 2 m long. If the speed of the boat is $2.00\text{ m/s}$, the magnitude of the induced e.m.f. in the rod is

The magnetic potential energy stored in certain inductor is $64 \times 10^{-3}\text{ J}$, when the current in the inductor is 80 mA. This inductor is of inductance

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If $I$ is the current in the circuit, then in the gap between the plates:

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3}\text{ m}^2$ and resistance $100\ \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $B = 0.5\text{ T}$ as shown. Work done in pulling the loop out of the field in $1.0\text{ s}$ is _________ $\times 10^{-6}\text{ J}$.

A cylindrical magnetic rod has length $5\text{ cm}$ and diameter $1\text{ cm}$. It has uniform magnetization $5.3 \times 10^{3}\text{ A/m}$. Its net magnetic dipole moment is nearly

The source of time varying magnetic field may be

(A) a permanent magnet

(B) an electric field changing linearly with time

(C) direct current

(D) a decelerating charge particle

(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

A horizontal wire of mass '$m$', length '$l$' and resistance '$R$' is sliding on the vertical rails on which uniform magnetic field '$B$' is directed perpendicular. The terminal speed of the wire as it falls under the force of gravity is ( $g =$ acceleration due to gravity)

A metal conductor of length $1\text{ m}$ rotates vertically about one of its ends at an angular velocity of $5\text{ rad/s}$. If horizontal component of earth's magnetic field is $0.2 \times 10^{-4}\text{ T}$, then the e.m.f. developed between the two ends of the conductor is

The magnetic dipole moment of a short magnetic dipole at a distant point along the equator of magnet has a magnitude of ' $X$ ' in SI units. If the distance between the point and the magnet is halved then the magnitude of dipole moment will be

A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm–1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10 $\Omega$ and air drag negligible, N will be close to:

A conducting square frame of side 'a' and a long straight wire carrying current $I$ are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity 'V'. The emf induced in the frame will be proportional to