Practice Questions

Q15.A circular coil has moment of inertia 0. 8 kg m2 around any diameter and is carrying current to produce a magnetic moment of 20 Am2 . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60o will be : (1) 10 rad s−1 (2) 10π rad s−1 (3) 20π rad s−1 (4) 20 rad s−1

Q15.An iron rod of volume 10−3 m3 and relative permeability 1000 is placed as core in a solenoid with 10 turns cm−1 . If a current of 0. 5 A is passed through the solenoid, then the magnetic moment of the rod will be : (1) 50 × 102 Am2 (2) 5 × 102 Am2 (3) 500 × 102 Am2 (4) 0. 5 × 102 Am2

Q16.A square loop of side 2a and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will be : (1) 2μ0I2a2 (2) 2μ0I2a2b πb π(a2+b2) (3) μ0I2a2b (4) μ0I2a2 2π(a2+b2) 2πb

Q16.An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 Ω resistor. The ratio of the currents at time t = ∞ and at t = 40 s is close to: (Take e2 = 7.389 ) (1) 1.06 (2) 1.15 (3) 1.46 (4) 0.84

Q16.If we need a magnification of 375 from a compound microscope of tube length 150mm and an objective of focal length 5mm, the focal length of the eye-piece, should be close to: (1) 22mm (2) 2mm (3) 4mm (4) 33mm

Q16.In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by ˆk and 2ˆi −2ˆj, respectively. What is the unit vector along direction of propagation of the wave. (1) + k) √2 1 (ˆi +ˆj) (2) √21 (ˆj (3) + 1 (ˆi √5 2ˆj) (4) √51 (2ˆi +ˆj)

Q16.The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 4 for this wavelength, will be: 3 (1) 15o (2) 30o (3) 45o (4) 60o

Q16.Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum: (1) λvisible < λmicro waves < λradio waves < λx-rays (2) λradio waves > λmicro waves > λvisible > λx-rays (3) λx-rays < λmicro waves < λradio waves < λvisible (4) λvisible > λx-rays > λradio waves > λmicro waves

Q16.A plane electromagnetic wave, has frequency of 2. 0 × 1010 Hz and its energy density is 1. 02 × 10−8 J m−3 in vacuum. The amplitude of the magnetic field of the wave is close to ( 4πε01 = 9 × 109 Nm2C2 ) and speed of light = 3 × 108 m s−1 . (1) 150 nT (2) 160 nT (3) 180 nT (4) 190 nT

Q16.A plane electromagnetic wave is propagating along the direction ˆi+ˆj , with its polarization along the direction √2 ˆk. The correct form of the magnetic field of the wave would be (here B0 is an appropriate constant): (1) ˆi−ˆj ˆi+ˆj (2) ˆj−ˆi ˆi+ˆj B0 −k B0 + k √2 cos(ωt √2 ) √2 cos(ωt √2 ) ˆi+ˆj ˆi+ˆj ˆi+ˆj −k −k B0 (3) B0ˆkcos(ωt √2 ) (4) √2 cos(ωt √2 )

Q16.An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown in the figure. The connector has length l. and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is (1) μ0 Iv ℓ (2) μ0 Iv ℓ 4π Rr π Rr (3) 2μ0 Iv ℓ (4) μ0 Iv ℓ π Rr 2π Rr

Q16.In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20m. The separation between P and Q is 5m and the phase of P is ahead of that of Q by 90°. A, B and C are three distinct point of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio : (1) 0 : 1 : 4 (2) 2 : 1 : 0 (3) 0 : 1 : 2 (4) 4 : 1 : 0

Q16.An electron is constrained to move along the y-axis with a speed of 0. 1 c (c is the speed of light) in the → presence of electromagnetic wave, whose electric field is E = 30ˆj sin(1. 5 × 107t −5 × 10−2x) V m−1. where t in in seconds and x is im meters.The maximum magnetic force experienced by the electron will be: (given c = 3 × 108 m s−1 and electron charge = 1. 6 × 10−19 Coloumbs (1) 3. 2 × 10−18 N (2) 2. 4 × 10−18 N (3) 4. 8 × 10−19 N (4) 1. 6 × 10−19 N

Q16.The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is → → E = E0 The magnetic field B, at the moment t = 0 is: jcos(ωt −kx). → → (1) E0 (2) B = B = E0√μ0ϵ0 √μ0ϵ0 cos(kx)ˆk cos(kx)ˆj (3) → (4) → E0 B = E0√μ0ε0 B = √μ0ϵ0 cos(kx)ˆk cos(kx)ˆj

Q16.A series L −R circuit is connected to a battery of emf V . If the circuit is switched on at t = 0, then the time at which the energy stored in the inductor reaches ( n1 ) times of its maximum value, is : (1) L √n (2) L √n+1 R ln( √n−1 ) R ln( √n−1 ) (3) L √n (4) L √n−1 R ln( √n+1 ) R ln( √n ) →

Q16.The electric fields of two plane electromagnetic plane waves in vacuum are given by E1→ = E0ˆj cos(ωt −kx) −→ and E2 = E0ˆk cos(ωt −ky) At t = 0, a particle of charge q is at origin with a velocity →v= 08cˆj ( c is the speed of light in vaccum). The instantaneous force experienced by the particle is: + + (1) E0q(0.8ˆi −ˆj 0.4ˆk) (2) E0q(0.4ˆi −3ˆj 0.8ˆk) (3) E0q(−0.8ˆi + ˆj + ˆk) (4) E0q(0.8ˆi + ˆj + 0.2ˆk)

Q16.In a Young's double slit experiment, light of 500 nm is used to produce and interference pattern. When the distance between the slits is 0. 05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to : (1) 0. 17° (2) 0. 57° (3) 1. 7° (4) 0. 07°

Q16.A plane electromagnetic wave of frequency 25GHz is propagating in vacuum along the z-direction. At a → particular point in space and time, the magnetic filed is given by B = 5 × 10−8 ˆj T. The corresponding electric → field E is (speed of light = 3 × 108 m s−1 ) (1) 1.66 × 10−16ˆi mV (2) −1.66 × 10−16ˆi mV (3) −15ˆi mV (4) 15ˆi mV

Q17.An electron, a doubly ionized helium ion ( He++ ) and proton are having the same kinetic energy. The relation between their respective de-Broglie wavelength λe*λHe++ and λp is : (1) λe > λHe++ > λp (2) λe < λHe++ == λp (3) λe > λp > λHe++ (4) λe < λp < λHe++

Q17.The magnifying power of a telescope with tube length 60cm is 5. What is the focal length of its eye piece? (1) 20cm (2) 40cm (3) 30cm (4) 10cm

Q17.A square loop of side 2a, and carrying current I is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about z-axis is given by. (1) μ0I 2a2 (2) μ0I 2a3 2πb 2πb2 (3) 2μ0I2a2 (4) 2μ0I2a3 πb πb2

Q17.When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to: JEE Main 2020 (03 Sep Shift 1) JEE Main Previous Year Paper (1) 0. 81 eV (2) 1. 02 eV (3) 0. 52 eV (4) 0. 61 eV

Q17.A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just 36% of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which JEE Main 2020 (07 Jan Shift 1) JEE Main Previous Year Paper the analyser needs to be rotated further, to reduce the output intensity to zero, is (sin−1( 35 ) = 37°) (1) 53o (2) 37o (3) 90o (4) 45o

Q17.In a Young's double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength 700 nm is used. If the wavelength of light is changed to 400 nm, the number of fringes observed in the same segment of the screen would be : (1) 24 (2) 30 (3) 18 (4) 28

Q17.A thin lens made of glass (refractive index = 1.5 ) of focal length f = 16cm is immersed in a liquid of refractive index 1.42 . If its focal length in liquid is fl , then the ratio fl/f is closest to the integer: (1) 1 (2) 9 (3) 5 (4) 17