Practice Questions

Q27.The magnetic field at the centre of a wire loop formed by two semicircular wires of radii 𝑅1 = 2𝜋 m and 𝑅2 = 4𝜋 m carrying current 𝐼= 4 A as per figure given below is 𝛼× 10-7 T. The value of 𝛼 is _____. (Centre O is common for all segments) JEE Main 2024 (27 Jan Shift 2) JEE Main Previous Year Paper

Q27.A solenoid of length 0.5 m has a radius of 1 cm and is made up of ' m ' number of turns. It carries a current of 5 A . If the magnitude of the magnetic field inside the solenoid is 6.28 × 10−3 T then the value of m is _____.

Q27.A circular coil having 200 turns, 2.5 × 10−4 m2 area and carrying 100μA current→ is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment (M) was directed along →B. Amount of work, required to rotate the coil through 90∘ from its initial orientation such that M becomes perpendicular to →B, is ______ μJ.

Q28.When a dc voltage of 100 V is applied to an inductor, a dc current of 5 A flows through it. When an ac voltage of 200 V peak value is connected to inductor, its inductive reactance is found to be 20√3Ω. The power dissipated in the circuit is _______ W.

Q28.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 m𝛺, the power dissipated by the loop as heat is ______ × 10-9 W .

Q28.A coil of 200 turns and area 0 . 20 m2 is rotated at half a revolution per second and is placed in uniform magnetic field of 0 . 01 T perpendicular to axis of rotation of the coil. The maximum voltage generated in the 2𝜋 coil is volt. The value of 𝛽 is ______. 𝛽 ∘

Q28.A straight magnetic strip has a magnetic moment of 44Am2 . If the strip is bent in a semicircular shape, its magnetic moment will be _______ Am2 . (given π = 227 )

Q28.A series LCR circuit with 𝐿= 100 mH, 𝐶= 10-3 F and 𝑅= 10 Ω, is connected across an AC source of 𝜋 𝜋 220 V, 50 Hz supply. The power factor of the circuit would be ____. o

Q28.The current of 5 A flows in a square loop of sides 1 m is placed in air. The magnetic field at the centre of the loop is X√2 × 10-7 T. The value of X is _________.

Q28.A small square loop of wire of side 𝑙 is placed inside a large square loop of wire of side 𝐿𝐿= 𝑙2. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is √𝑥× 10-7 H, where 𝑥= ______.

Q28.When a coil is connected across a 20 V dc supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz ac supply, it draws a current of 4 A. The self inductance of the coil is ______ mH . ( Take π = 3 )

Q28.A alternating current at any instant is given by i = [6 + √56 sin(100πt + π/3)] A. The rms value of the current is ________ A.

Q28.In the given figure, the charge stored in 6μF capacitor, when points A and B are joined by a connecting wire is _______ μC. o

Q28.The horizontal component of earth's magnetic field at a place is 3. 5 × 10−5 T. A very long straight conductor carrying current of √2 A in the direction from South east to North West is placed. The force per unit length experienced by the conductor is ________ ×10−6 N m−1 .

Q28.A square loop of side 10 cm and resistance 0. 7 Ω is placed vertically in the east-west plane. A uniform magnetic field of 0. 20 T is set up across the plane in the north-east direction. The magnetic field is decreased to zero in 1 s at a steady rate. Then, the magnitude of induced emf is √x × 10−3 V . The value of x is _______.

Q28.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 12mV . The self-inductance of the inductor _____ mH .

Q28.The magnetic flux 𝜙 (in weber) linked with a closed circuit of resistance 8 𝛺 varies with time (in seconds) as 𝜙= 5𝑡2 −36𝑡+ 1. The induced current in the circuit at 𝑡 = 2 s is _______ A.

Q28.An alternating emf E = 110√2 sin 100t volt is applied to a capacitor of 2μF, the rms value of current in the circuit is _____ mA ,

Q28.A square loop PQRS having 10 turns, area 3.6 × 10−3 m2 and resistance 100Ω is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper the field in 1.0 s is ______ ×10−6 J.

Q28.For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 25nF. If resistance of 200Ω and 100mH inductor is being used in the given circuit. The frequency of ac source is ______ ×103 Hz . (given π2 = 10 )

Q28.Two coils have mutual inductance 0. 002 H. The current changes in the first coil according to the relation i = i0sinωt, where i0 = 5 A and ω = 50π rad s−1 . The maximum value of emf in the second coil is απ V . The value of α is

Q28.An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20μF is _____V.

Q28.A rod of length 60 cm rotates with a uniform angular velocity 20rads−1 about its perpendicular bisector, in a uniform magnetic filed 0.5T . The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _____V.

Q29.A light ray is incident on a glass slab of thickness 4√3 cm and refractive index √2 . The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is _____ cm . ( Given sin 15∘= 0.25)

Q29.Two coherent monochromatic light beams of intensities I and 4I are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is xI . The value of x is $_________.