Practice Questions

Q14.In LC circuit the inductance L = 40 mH and capacitance C = 100 μF. If a voltage V (t) = 10sin(314t) is applied to the circuit, the current in the circuit is given as: (1) 0.52 cos(314t) (2) 10 cos(314t) (3) 5.2 cos(314t) (4) 0.52 sin(314t)

Q14.In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point B with respect to the point A is: (1) +2V (2) −2V (3) –1V (4) +1V

Q14.Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of 1012 m/s2 by an applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is 1.6 × 10−27kg ) (1) 0.71mT (2) 7.1mT (3) 0.071mT (4) 71mT

Q14.A LCR circuit behaves like a clamped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be: (1) L ↔m, C ↔k, R ↔b (2) L ↔1b , C ↔ m1 , R ↔1k (3) L ↔k, C ↔b, R ↔m (4) L ↔m, C ↔1k , R ↔b

Q15.A charged particle going around in a circle can be considered to be a current loop. A particle of a mass m → carrying charge q is moving in a plane with speed v under the influence of magnetic field B. The magnetic moment of this moving particle is : B (1) mv2→ B (2) −mv2→ 2B2 2πB2 B (3) −mv2→ B (4) −mv2→ B2 2B2

Q15.At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced JEE Main 2020 (08 Jan Shift 1) JEE Main Previous Year Paper EMF in the loop is: (1) 56μV (2) 28μV (3) 48μV (4) 36μV

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

Q15. As shown in the figure, a battery of emf ∈ is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = tc ( tc is the time constant of the circuit) is: (1) ∈L (2) ∈L eR2 R2 (1 −1e ) (3) ∈L (4) ∈R R2 eL2

Q15.Two identical capacitors A and B, charged to the same potential 5V are connected in two different circuits as shown below at time t = 0. If the charge on capacitors A and B at time t = CR is QA and QB respectively, then (Here e is the base of natural logarithm) (1) QA = VeC , QB = CV2 (2) QA = V C, QB = CV (3) QA = V C, QB = VeC (4) QA = CV2 , QB = VeC

Q15.A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dB /dt = 0. 032 Ts−1. The induced current in the loopis close to (Resistivity of the metal wire is 1. 23 × 10−8 Ωm ) (1) 0.43 A (2) 0.61 A (3) 0.34 A (4) 0.53 A

Q15.If the magnetic field in a plane electromagnetic wave is given by → B = 3 × 10−8 sin(1.6 × 103x + 48 × 1010t)ˆjT, then what will be expression for electric field ? → → (1) V (2) V E = E = (60 sin(1.6 × 103x + 48 × 1010t)ˆk m ) (9 sin(1.6 × 103x + 48 × 1010t)ˆk m ) (3) → V (4) → V E = E = (3 × 10−8 sin(1.6 × 103x + 48 × 1010t)ˆj m ) (3 × 10−8 sin(1.6 × 103x + 48 × 1010t)ˆi m )

Q15.An inductance coil has a reactance of 100 Ω . When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45°. The self-inductance of the coil is (1) 1. 1 × 10−2 H (2) 1. 1 × 10−1 H (3) 5. 5 × 10−5 H (4) 6. 7 × 10−7 H JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q15.The magnetic field of a plane electromagnetic wave is B = 3 × 10−8 sin[200π(y + ct)]ˆi T . Where, c = 3 × 108 m s−1 is the speed of light the corresponding electric filed is : → → (1) (2) E = 9 + V/m E = −10−6 + V/m sin[200π(y ct)ˆk sin[200π(y ct)ˆk (3) → (4) → E = 3 × 10−8 + V/m E = −9 + V/m sin[200π(y ct)ˆk sin[200π(y ct)ˆk

Q15.Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required? (1) T : Large retentivity, small coercivity (2) P : small retentivity, large coercivity (3) T : Large retentivity, large coercivity (4) P : large retentivity, large coercivity

Q15.A planar loop of wire rotates in a uniform magnetic field. Initially, at t = 0 , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at: (1) 2.5 s and 7.5 s (2) 2.5 s and 5.0 s (3) 5.0 s and 7.5 s (4) 5.0 s and 10. 0 s

Q15.A point like object is placed at distance of 1m in front of a convex lens of focal length 0. 5m. A plane mirror is placed at a distance of 2m behind the lens. The position and nature of the image formed by the system is (1) 2. 6m from the mirror, real (2) 1m from the mirror, virtual (3) 1m from the mirror, real (4) 2. 6m from the mirror, virtual

Q15.A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil? Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit. JEE Main 2020 (04 Sep Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)

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 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.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.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

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.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.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.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)