Practice Questions

Q23.A circuit connected to an ac source of emf e = e0sin⁡100𝑡 with t in seconds, gives a phase difference of 𝜋 4 between the emf 𝑒 and current i . Which of the following circuits will exhibit this? (1) RC circuit with R = 1 kΩ and C = 1 μF (2) RL circuit with R = 1 kΩ and L = 1 mH (3) RL circuit with R = 1 kΩ and L = 10 mH (4) RC circuit with R = 1 kΩ and C = 10 μF

Q23.A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is 30 mV , then the amplitude of the electric field for the wave propagating in the glass medium will be: (1) 30 mV (2) 6 mV (3) 24 mV (4) 10 mV

Q23.The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to: (1) L (2) 1 L2 (3) 1 (4) L2 L JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper →

Q23.A coil of self inductance 10 mH and resistance of 0.1 Ω is connected through a switch to a battery of internal resistance 0.9 Ω . After the switch is closed, the time taken for the current to attain 80% of the saturation value is: [ln5 = 1.6] (1) 0.103 s (2) 0.002 s (3) 0.324 s (4) 0.016 s

Q23.Sunlight of intensity 50 W m−2 is incident normally on the surface of a solar panel. Some part of incident energy ( 25%) is reflected from the surface and the rest is absorbed. The force exerted on 1 m2 surface area will be close to (c = 3 × 108 m s−1) (1) 15 × 10−8 N (2) 20 × 10−8 N (3) 10 × 10−8 N (4) 35 × 10−8 N

Q23.A plano - convex lens (focal length f2 , refractive index μ2, radius of curvature R) fits exactly into a plano - concave lens (focal length f1, refractive index μ1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be: R (1) (2) f1 −f2 μ2 − μ1 (3) f1 + f2 (4) f1+f22f1f2

Q23.A transparent cube of side d, made of a material of refractive index μ2 , is immersed in a liquid of refractive index μ1 ( μ1 < μ2). A ray is incident on the face AB at an angle θ (shown in the figure). Total internal reflection takes place at the point E on the face BC. Then, θ must satisfy (1) (2) θ > sin−1 μ2 θ < sin−1 2 −1 √μ2μ21 μ1 (3) θ < sin−1 μ1 (4) 2 μ2 θ > sin−1 −1 √μ2μ21

Q23.An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is 𝑎 and distance of its centre from the wire is 𝑑 𝑑≫𝑎. If the loop applies a force 𝐹 on the wire then: 2 (1) 𝐹∝𝑎 (2) 𝐹= 0 𝑑 𝑎 (3) 𝐹∝𝑎2 (4) 𝐹∝ 𝑑 𝑑3

Q23.An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s the speed and direction of the image will be (1) 2.26 × 10−3 m/s away from the lens (2) 0.92 × 10−3 m/s away from the lens (3) 3.22 × 10−3 m/s towards the lens (4) 1.16 × 10−3 m/s towards the lens

Q23.The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10A to 25A in 1s , the change in the energy of the inductance is: (1) 637.5 J (2) 740 J (3) 437.5 J (4) 540 J

Q23.An electromagnetic wave is represented by the electric filed →E = E0^nsin⁡ωt + 6𝑦- 8𝑧. Taking unit vectors in 𝑥, 𝑦 and 𝑧 directions to be ^𝑖, ^𝑗, ^𝑘, the directions of propogations ^s, is: (1) 3^𝑖- 4^𝑗 (2) -3^𝑖+ 4^𝑗 ^s = ^s = 5 5 4^𝑖- 3^𝑘 -4^𝑖- 3^𝑘 (3) (4) ^s = ^s = 5 5

Q23.A 27 mW laser beam has a cross-sectional area of 10 mm2 . The magnitude of the maximum electric field in this electromagnetic wave is given by: [Given permittivity of space ϵ0 = 9 × 10−12SI units, Speed of light c = 3 × 108 m/s] (1) 2kV/m (2) 0.7kV/m (3) 1kV/m (4) 1.4kV/m

Q23.The electric field of a plane electromagnetic wave is given by → E = E0ˆi cos(kz)cos(ωt) → The corresponding magnetic field B is then given by: (1) → E0 (2) → E0 B = C ˆj B = C ˆk cos(kz)sin(ωt) sin(kz)cos(ωt) (3) → E0 (4) → E0 B = C ˆj B = C ˆj sin(kz)sin(ωt) sin(kz)cos(ωt)

Q23.A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 V m-1 along y-direction. Its corresponding magnetic field component, B would be: (1) 2 × 10-8 T along z- (2) 2 × 10-8 T along y- (3) 6 × 10-8 T along z- (4) 6 × 10-8 T along x- direction direction direction direction

Q24.Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is finally reflected from the second mirror (M2) and parallel to the first mirror (M1). The angle between the two mirrors will be: (1) 60o (2) 45o (3) 90o (4) 75o

Q24.A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances x1 and x2(x1 > x2) from the lens. The ratio of x1 and x2 is: (1) 2 : 1 (2) 5 : 3 (3) 4 : 3 (4) 3 : 1

Q24.A plano-convex lens of refractive index μ1 and focal length f1 is kept in contact with another plano-concave lens of refractive index μ2 and focal length f2. If the radius of curvature of their spherical faces is R each and f1 = 2f2, the μ1 and μ2 are related as: (1) 2μ2 −μ1 = 1 (2) 3μ2 −2μ1 = 1 (3) μ1 + μ2 = 3 (4) 2μ1 −μ2 = 1

Q24.The magnetic field of an electromagnetic wave is given by: →B = 1.6 × 10-6cos⁡ 2 × 107𝑧+ 6 × 1015𝑡 2^𝑖+ ^𝑗 Wb m2 The associated electric field will be: (1) →E = 4.8 × 102 cos 2 × 107𝑧- 6 × 1015𝑡 -2 ^𝑗+ ^𝑖 V(2) →E = 4.8 × 102 cos 2 × 107𝑧+ 6 × 1015𝑡 ^𝑖- 2 ^𝑗 V m m (3) →E = 4.8 × 102 cos 2 × 107𝑧+ 6 × 1015𝑡 -^𝑖+ 2^𝑗V →E = 4.8 × 102 cos 2 × 107𝑧- 6 × 1015𝑡 2^𝑖+ ^𝑗V m(4) m

Q24.The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by the → → expression E(x, y) = 10ˆjcos(6x + 8z). The magnetic field B(x, z, t) is given by ( c is the velocity of light.) (1) 1 + cos(6x + 8z −10 ct) c (6ˆk −8ˆi) cos(6x + 8z + 10 ct) (2) 1c (6ˆk 8ˆi) (3) 1 + + 8z −10 ct) c (6ˆk 8ˆi) cos(6x −8z + 10 ct) (4) 1c (6ˆk −8ˆi)cos(6x

Q24.A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is √3, then the angle of incidence is : (1) 90∘ (2) 30∘ (3) 60∘ (4) 45∘

Q24.A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is: (1) 2√3 a + 2b (2) 2a + 2b (3) 2a + 2b (4) 2a + 2b3 √3

Q24.A system of three polarizers P1, P2, P3 is set up such that the pass axis of P3 is crossed with respect to that of P1 . The pass axis of P2 is inclined at 60o to the pass axis of P3. When a beam of unpolarized light of intensity Io is incident on P1, the intensity of light transmitted by the three polarizers is I . The ratio (Io/I) equals (nearly): (1) 5.33 (2) 16.00 (3) 1.80 (4) 10.67

Q24.In figure, the optical fiber is 𝑙= 2 m long and has a diameter of d = 20 μm . If a ray of light is incident on one end of the fiber at angle θ1 = 40° , the number of reflections it makes before emerging from the other end is close to: (refractive index of fiber is 1.31 , sin 40° = 0.64 and sin-1⁡0.49 = 30° .) (1) 55000 (2) 57000 (3) 45000 (4) 66000

Q24.The magnetic field of a plane electromagnetic wave is given by B = B0ˆi[cos(kz −ωt)] + B1ˆjcos(kz + ωt) , where B0 = 3 × 10–5 T and B1 = 2 × 10–6 T . The RMS value of the force experienced by a stationary charge Q = 10–4 C at z = 0 is closest to (1) 0.1 N (2) 0.9 N (3) 3 × 10–2 N (4) 0.6 N

Q24.What is the position and nature of image formed by lens combination shown in figure? ( f1, f2 are focal lengths) (1) 40 cm from point B at right; real (2) 203 cm from point B at right, real (3) 70 cm from point B at right; real (4) 70 cm from point B at left; virtual JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper