Practice Questions

Q27.An electron moves through a uniform magnetic field →𝐵= 𝐵0 ^i + 2𝐵0 ^j T. At a particular instant of time, the → velocity of electron is →𝑢= 3 ^i + 5 ^j m s-1. If the magnetic force acting on electron is 𝐹= 5𝑒 ^k N, where 𝑒 is the charge of electron, then the value of 𝐵0 is ____ T.

Q27.A 2 A current carrying straight metal wire of resistance 1Ω, resistivity 2 × 10−6Ωm , area of cross-section 10 mm2 and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field →B . The magnitude of B is _____ ×10−1 T (given, g = 10 m/s2 ). JEE Main 2024 (05 Apr Shift 1) JEE Main Previous Year Paper

Q27.Two circular coils 𝑃 and 𝑄 of 100 turns each have same radius of 𝜋 cm. The currents in 𝑃 and 𝑅 are 1 A and 2 A respectively. 𝑃 and 𝑄 are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is √𝑥 mT, where 𝑥= ______. [Use 𝜇0 = 4𝜋× 10−7 T m A−1]

Q27.A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0. 5 G and angle of dip is 30°. The emf induced across the blades is Nπ × 10−5 V . The value of N is _______.

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.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.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.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 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.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.

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

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.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.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.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.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.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 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.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.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.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 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 ∘

Q29.Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper single slit pattern is _____ ×10−4 m