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JEE Mains | PYQ

In the given figure, an inductor and a resistor are connected in series with a battery of emf \( E \) volt. \( \dfrac{E^{a}}{2b} \, \text{J/s} \) represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of \( \dfrac{b}{a} \) will be ______.

The induced emf can be produced in a coil by:
A. moving the coil with uniform speed inside uniform magnetic field
B. moving the coil with non-uniform speed inside uniform magnetic field
C. rotating the coil inside the uniform magnetic field
D. changing the area of the coil inside the uniform magnetic field
Choose the correct answer from the options given below:

Three identical resistors with resistance \( R = 12 \, \Omega \) and two identical inductors with self inductance \( L = 5 \, \text{mH} \) are connected to an ideal battery with emf of \( 12 \, \text{V} \) as shown in figure. The current through the battery long after the switch has been closed will be ________ \( \text{A} \).

A coil has an inductance of \( 2 \, \text{H} \) and resistance of \( 4 \, \Omega \). A \( 10 \, \text{V} \) is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ________ \( \times 10^{-2} \, \text{J} \).

Two concentric circular with radii \( 1 \, \text{cm} \) and \( 1000 \, \text{cm} \), and number of turns \( 10 \) and \( 200 \) respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be __________ \( \times 10^{-8} \, \text{H} \). (Take, \( \pi^{2} = 10 \))

A \( 12 \, \text{V} \) battery connected to a coil of resistance \( 6 \, \Omega \) through a switch, drives a constant current in the circuit. The switch is opened in \( 1 \, \text{ms} \). The emf induced across the coil is \( 20 \, \text{V} \). The inductance of the coil is:

An insulated copper wire of \( 100 \) turns is wrapped around a wooden cylindrical core of the cross-sectional area \( 24 \, \text{cm}^2 \). The two ends of the wire are connected to a resistor. The total resistance in the circuit is \( 12 \, \Omega \). If an externally applied uniform magnetic field in the core along its axis changes from \( 1.5 \, \text{T} \) in one direction to \( 1.5 \, \text{T} \) in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ____________ \( \text{mC} \).

A metallic cube of side \( 15 \, \text{cm} \) moving along \( y \)-axis at a uniform velocity of \( 2 \, \text{m s}^{-1} \). In a region of uniform magnetic field of magnitude \( 0.5 \, \text{T} \) directed along \( z \)-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be ________ \( \text{mV} .\)

A conducting circular loop of radius \( \frac{10}{\sqrt{\pi}} \, \text{cm} \) is placed perpendicular to a uniform magnetic field of \( 0.5 \, \text{T} \). The magnetic field is decreased to zero in \( 0.5 \, \text{s} \) at a steady rate. The induced emf in the circular loop at \( 0.05 \, \text{s} \) is:

A \( 20 \, \text{cm} \) long metallic rod is rotated with \( 210 \, \text{rpm} \) about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field \( 0.2 \, \text{T} \) parallel to the axis exists everywhere. The emf developed between the centre and the ring is __________ \( \text{mV} \).
Take \( \pi = \dfrac{22}{7} \)

A conducting circular loop is placed in a uniform magnetic field of \( 0.4 \, \text{T} \) with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of \( 1 \, \text{mm/s} \). The magnitude of induced emf in the loop at an instant when the radius of loop is \( 2 \, \text{cm} \) will be ___ \( \mu \text{V} \).

A \( 1 \, \text{m} \) long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \( 0.15 \, \text{T} \). If the resistance of the circuit is \( 5 \, \Omega \), the force needed to move the rod in direction, as indicated, with a constant speed of \( 4 \, \text{m/s} \) will be ______ \( 10^{-3} \, \text{N} \).

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes \( x \) times its initial resonant frequency \( \omega_{0} \). The value of \( x \) is:

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:

The energy of an electromagnetic wave contained in a small volume oscillates with:

A square loop of side \( 2.0 \, \text{cm} \) is placed inside a long solenoid that has \( 50 \) turns per centimeter and carries a sinusoidally varying current of amplitude \( 2.5 \, \mathring{A}. \) and angular frequency \( 700 \, \text{rad s}^{-1} \). The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is \( x \times 10^{-4} \, \text{V} \). The value of \( x \) is ______.

Given below are two statements:
Statement I: The diamagnetic property depends on temperature.
Statement II: The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field.
In the light of given statements, choose the correct answer from the options given below.

A metallic rod of length ‘L’ is rotated with an angular speed of \( '\omega' \) normal to a uniform magnetic field ‘B’ about an axis passing through one end of rod as shown in figure. The induced emf will be:

Match List I with List II:

Choose the correct answer from the options given below:

The magnetic field \( B \) crossing normally a square metallic plate of area \( 4 \, \text{m}^2 \) is changing with time as shown in figure. The magnitude of induced emf in the plate during \( t = 2 \, \text{s} \) to \( t = 4 \, \text{s} \), is _______ \( \text{mV} \).

Spherical insulating ball and spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction)

An emf of \( 0.08 \, \text{V} \) is induced in a metal rod of length \( 10 \, \text{cm} \) held normal to a uniform magnetic field of \( 0.4 \, \text{T} \), when moves with a velocity of:

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field \( B = 0.8 \, \text{T} \). When released the radius of the loop starts shrinking at a constant rate of \( 2 \, \text{cm s}^{-1} \). The induced emf in the loop at an instant when the radius of the loop is \( 10 \, \text{cm} \) will be ______ \( \text{mV} \).