Practice Questions

Q19.A proton and an α - particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2 ) are accelerated from rest through a potential difference V . If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp : rα of the circular paths described by them will be: (1) 1 : 3 (2) 1 : √2 (3) 1 : 2 (4) 1 : √3

Q19.In free space, a particle 𝐴 of charge 1 μC is held fixed at point 𝑃 . Another particle 𝐵 of the same charge and mass 4 μg is kept at a distance of 1 mm from 𝑃. If 𝐵 is released, then its velocity at a distance of 9 mm from 𝑃 is: [Take 1 = 9 × 109 N m2 C-2 ] 4πϵ0 (1) 1.0 m s-1 (2) 1.5 × 102 m s-1 (3) 2.0 × 103 m s-1 (4) 3.0 × 104 m s-1

Q19.A circular coil having N turns and radius r carries a current I . It is held in the XZ plane in a magnetic field B^i . The torque on the coil due to the magnetic field is: (1) Bπr2IN (2) Br2I (3) Bπr2I (4) Zero πN N

Q19.A 2 W carbon resistor is color coded with green, black, red and silver respectively. The maximum current which can be passed through this resistor is: (1) 100 mA (2) 0.4 mA (3) 20 mA (4) 63 mA

Q19.A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 × 10−6 J/T when a magnetic intensity of 60 × 103 A/m is applied. Its magnetic susceptibility is: JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper (1) 3.3 × 10−2 (2) 4.3 × 10−2 (3) 2.3 × 10−2 (4) 3.3 × 10−4 →

Q19.The actual value of resistance R , shown in the figure is 30Ω. This is measured in an experiment as shown using the standard formula R = VI , where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5% less, then the internal resistance of the voltmeter is: (1) 35Ω (2) 600Ω (3) 570Ω (4) 350Ω

Q19.Determine the charge on the capacitor in the following circuit: (1) 2 μC (2) 60 μC (3) 10 μC (4) 200 μC

Q19.A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 × 10−19C ) (1) 9.1 × 10−31 kg (2) 1.6 × 10−27 kg (3) 2.0 × 10−24 kg (4) 1.6 × 10−19 kg

Q19.Two wires A & B are carrying currents I1 and I2 as shown in the figure. The separation between them is d . A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are: (1) x = ± and x = I2 d (I1−I2) (I1−I2) I1d (2) x = ( I1+I2I1 )d (3) x = ( I1+I2I2 )d and x = ( I1−I2I2 )d (4) x = ( I1−I2I1 )d and x = (I1+I2)I2 d

Q19.The resistive network shown below is connected to a D . C . source of 16 V . The power consumed by the network is 4 Watt. The value of R is: (1) 16 Ω (2) 8 Ω (3) 6 Ω (4) 1 Ω

Q20.One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop (BL) to that at the centre of the coil (BC), i.e. BL will be BC 1 (1) 2 (2) N1 N (3) N (4) N 2

Q20.A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let rp, re and rHe be their respective radii, then, (1) re > rp = rHe (2) re < rp = rHe (3) re < rp < rHe (4) re > rp > rHe

Q20.There are two long co-axial solenoids of same length l. The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2 , respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is : (1) n1 (2) n2 ⋅r1 n2 n1 r2 n2 (3) n2 2 (4) ⋅r2 n1 n1 r21

Q20.As shown in the figure, two infinitely long, identical wires are bent by 90o and placed in such a way that the segments LP and QM are along the x - axis, while segments PS and QN are parallel to the y - axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10−4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be (μ0 = 4π × 10−7NA−2) : (1) 20 A, perpendicular into the page (2) 20 A, perpendicular out of the page (3) 40 A, perpendicualr into the page (4) 40 A, perpendicular out of the page JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper

Q20.Space between two concentric conducting spheres of radii a and b ( b > a ) is filled with a medium of resistivity ρ . The resistance between the two spheres will be: ρ 1 1 ρ 1 1 (1) + (2) + 4π a b 2π a b ρ 1 1 ρ 1 1 (3) - (4) - 4π a b 2π a b

Q20.A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45° and 40 times per minute where the dip is 30°. If 𝐵1 and 𝐵2 are the net magnetic fields due to the earth at the two places respectively, then the ratio B1 / B2 is approximately equal to (1) 3.6 (2) 1.8 (3) 1.2 (4) 0.7

Q20.A magnet of total magnetic moment 10−2 ˆi A m2 is placed in a time varying magnetic field, Bˆi(cos ωt) where B = 1 Tesla and ω = 0.125 rad s−1 . The work done for reversing the direction of the magnetic moment at JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper t = 1 second, is: (1) 0.007 J (2) 0.02 J (3) 0.014 J (4) 0.01 J

Q20.A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 m s−1, at right angles to the horizontal component of the earth's magnetic field of 0.3 × 10−4 Wb m−2. The value of the induced emf in the wire is: (1) 0.3 × 10−3 V (2) 1.1 × 10−3 V (3) 2.5 × 10−3 V (4) 1.5 × 10−3 V

Q20.In the figure shown, what is the current (in Ampere) drawn from the battery? You are given: 𝑅1 = 15 Ω , 𝑅2 = 10 Ω , 𝑅3 = 20 Ω , 𝑅4 = 5 Ω, 𝑅5 = 25 Ω, 𝑅6 = 30 Ω, 𝐸= 15 V (1) 9 / 32 (2) 7 / 18 (3) 13 / 24 (4) 20 / 3

Q20.Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A. (See figure) (μ0 = 4π × 10−7 NA−2) (1) 1.5 × 10−5 T (2) 2.0 × 10−5 T (3) 3.0 × 10−5 T (4) 2.5 × 10−5 T

Q21.In the circuit shown, the switch S1 is closed at time t = 0 and the switch S2 is kept open. At some later time (t0), the switch S1 is opened and S2 is closed. the behaviour of the current I as a function of time ' t ' is given by: JEE Main 2019 (11 Jan Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)

Q21.A particle of mass m and charge q is in an electric and magnetic field given by → → E = 2^i + 3^j; B = 4^j + 6^k The charged particle is shifted from the origin to the point P(x = 1; y = 1) along a straight path. The magnitude of the total work done is : (1) (0.35)q (2) 5q (3) (2.5) q (4) (0.15)q

Q21.A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW . If the current in the secondary coil is 10 A , then the input voltage and current in the primary coil are: (1) 440 V and 20 A (2) 220 V and 20 A (3) 440 V and 5 A (4) 220 V and 10 A JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper

Q21.A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5 A and its efficiency is 90 % , the output current would be: (1) 35 A (2) 25 A (3) 50 A (4) 45 A

Q21.A 20 H inductor coil is connected to a 10 Ω resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is: (1) 1 (2) 2ln2 (3) 2 (4) ln2 2ln2 ln2