Practice Questions

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 cell of internal resistance r drives current through an external resistance R . The power delivered by the cell to the external resistance will be maximum when: (1) R = 2r (2) R = r (3) R = 1000 r (4) R = 0.001 r

Q19.In a conductor, if the number of conduction electrons per unit volume is 8.5 × 1028 m−3 and mean free time is 25 fs (femto second), it’s approximate resistivity is: (me = 9.1 × 10−31 kg) (1) 10−7 Ω m (2) 10−6 Ω m (3) 10−5 Ω m (4) 10−8 Ω m

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

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

Q20.A moving coil galvanometer has resistance 50 Ω and it indicates full deflection at 4 mA current. A voltmeter is made using this galvanometer and a 5 kΩ resistance. The maximum voltage, that can be measured using this voltmeter, will be close to: (1) 40 V (2) 15 V (3) 20 V (4) 10 V

Q20.The Wheatstone bridge shown in the figure below, gets balanced when the carbon resistor used as R1 has the colour code (orange, red, brown). The resistors R2 and R4 are 80 Ω and 40 Ω , respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as R3 , would be JEE Main 2019 (10 Jan Shift 2) JEE Main Previous Year Paper (1) brown, blue, black. (2) brown, blue, brown. (3) grey, black, brown. (4) red, green, brown.

Q20.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 N m-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 10Ω and air drag negligible, JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper N will be close to: (1) 1000 (2) 5000 (3) 10000 (4) 50000

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.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.The region between y = 0 and y = d contains a magnetic field B = B^z. A particle of mass m and charge q mv , the acceleration of the charged particle at the point of its enters the region with a velocity →v = v^i. if d = 2qB emergence at the other side is : (1) qv m B ( 12^i −√32 ^j) (2) qvmB ( √32 ^i + 12 ^j) (3) qv B −^j+^i (4) None of the above m ( √2 )

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.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.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.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 resistance is shown in the figure. Its value and tolerance are given respectively by: (1) 27 𝑘Ω, 10% (2) 270 Ω, 5% (3) 270 Ω, 10% (4) 27 𝑘Ω, 20%

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

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.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.Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of 10−3 Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is: (1) 3.67 × 10−3 Wb (2) 6.67 × 10−4 Wb (3) 3.67 × 10−4 Wb (4) 6.67 × 10−3 Wb

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

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

Q21.A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is: (1) 11 × 105 W (2) 11 × 10−3 W (3) 11 × 10−5 W (4) 11 × 10−4 W

Q21.An insulating thin rod of length l has a linear charge density ρ(x) = ρ0 xl on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is: (1) π n ρ0l3 (2) n ρ0l3 4 (3) π n ρ0 l3 (4) π3 n ρ0l3