Faraday's and Lenz's Law PYQs: JEE Mains Physics

Showing 1–31 of 31 questions

1. 1. A \(30\) cm long solenoid has \(10\) turns per cm and area of \(5\) cm\(^2\). The current through the solenoid coil varies from \(2\) A to \(4\) A in \(3.14\) s. The e.m.f. induced in the coil is \(\alpha\times 10^{-5}\) V. The value \(\alpha\) is ________. 2026 Medium
2. 2. A block takes \(t\) time to slide down a plane inclined at \(45°\) to the horizontal. If the surface is made smooth (frictionless), the block takes time \(\dfrac{t}{2}\) to slide down the plane. The coefficient of friction between the block and the inclined plane is \(\left(\dfrac{\alpha}{100}\right)\). The value of \(\alpha\) is __________. 2026 Hard
3. 3. A circular loop of radius \(20\text{ cm}\) and resistance \(2\ \Omega\) is placed in a time varying magnetic field \(\vec{B} = (2t^2 + 2t + 3)\text{ T}\). At \(t = 0\), for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at \(t = 3\text{ s}\) is \(\dfrac{\alpha}{50}\text{ A}\). The value of \(\alpha\) is _______.
   (Take \(\pi = 22/7\)) 2026 Medium
4. 4. A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is ___________ mV. 2026 Medium
5. 5. A square loop of side \(2\) cm is placed in a time varying magnetic field with magnitude as \(B = 0.4\sin(300t)\) Tesla. The normal to the plane of loop makes an angle of \(60°\) with the field. The maximum induced emf produced in the loop is __________ mV. 2026 Hard
6. 6. Three identical coils \(C _1, C _2\) and \(C _3\) are closely placed such that they share a common axis.\(C _2\) is exactly midway.\(C _1\) carries current I in anti-clockwise direction while \(C _3\) carries current I in clockwise direction. An induced current flows through \(C _2\), will be in clockwise direction when 2026 Medium
7. 7. When a coil is placed in a time dependent magnetic field the power dissipated in it is \(P\). The number of turns, area of the coil and radius of the coil wire are \(N\), \(A\) and \(r\) respectively. For a second coils number of turns, area of the coil and radius of the coil wire are \(2N\), \(2A\) and \(3r\) respectively. When the first coil is replaced with second coil the power dissipated in it is \(\sqrt{2}\,\alpha P\). The value of \(\alpha\) is _______. 2026 Hard
8. 8. A coil is placed perpendicular to a magnetic field of 5000 T . When the field is changed to 3000 T in 2 s , an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m , then the number of turns in the coil is _______. 2024 Medium
9. 9. A square loop of side \(10 \mathrm{~cm}\) and resistance \(0.7\  \Omega\) is placed vertically in east-west plane. A uniform magnetic field of \(0.20 \mathrm{~T}\) is set up across the plane in north east direction. The magnetic field is decreased to zero in \(1 \mathrm{~s}\) at a steady rate. Then, magnitude of induced emf is \(\sqrt{\mathrm{x}} \times 10^{-3} \mathrm{~V}\). The value of \(x\) is _______. 2024 Hard
10. 10. The magnetic flux \(\phi\) (in weber) linked with a closed circuit of resistance \(8\  \Omega\) varies with time (in seconds) as \(\phi=5 t^2-36 t+1\). The induced current in the circuit at \(t=2 \mathrm{~s}\) is _______ \(\mathrm{A}\). 2024 Hard
11. 11. A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will 2023 Medium
12. 12. A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field \(B =0.8\,T\). When released the radius of the loop starts shrinking at a constant rate of \(2\,cm ^{-1}\). The induced emf in the loop at an instant when the radius of the loop is \(10\,cm\) will be \(........mV\). 2023 Medium
13. 13. A conducting circular loop is placed in a uniform magnetic field of \(0.4\,T\) with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of \(1\,mm / s\). The magnitude of induced emf in the loop at an instant when the radius of the loop is \(2\,cm\) will be \(...........\,\mu V\). 2023 Medium
14. 14. A conducting loop of radius \(\frac{10}{\sqrt{\pi}}\,cm\) is placed perpendicular to a uniform magnetic field of \(0.5\,T\). The magnetic field is decreased to \(zero\) in \(0.5\,s\) at a steady rate. The induced emf in the circular loop at \(0.25\,s\) is: 2023 Medium
15. 15. A metallic rod of length ' \(L\) ' is rotated with an angular speed of ' \(\omega\) ' normal to a uniform magnetic field ' \(B\) ' about an axis passing through one end of rod as shown in figure. The induced emf will be :
    2023 Medium
16. 16. An insulated copper wire of \(100\) turns is wrapped around a wooden cylindrical core of the crosssectional area \(24\,cm ^2\). The two ends of the wire are connected to a resistor. The total resistance in the circuit is \(12\,\Omega\). If an externally applied uniform magnetic field in the core along its axis changes from \(1.5 T\) in one direction to \(1.5\,T\) in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be \(.........\,mC\). 2023 Medium
17. 17. The magnetic field \(B\) crossing normally a square metallic plate of area \(4\,m ^2\) is changing with time as shown in figure. The magnitude of induced \(emf\) in the plate during \(t=2\,s\) to \(t=4\,s\), is \(..........\,mV\)
    2023 Hard
18. 18. A conducting circular loop is placed in \(X - Y\) plane in presence of magnetic field \(\overrightarrow{ B }=\left(3 t ^{3} \hat{ j }+3 t ^{2} \hat{ k }\right)\) in SI unit. If the radius of the loop is \(1 m\), the induced emf in the loop, at time, \(t =2\,s\) is \(n \pi V\). The value of \(n\) is. 2022 Medium
19. 19. In a coil of resistance \(8 \Omega\), the magnetic flux due to an external magnetic field varies with time as \(\phi=\frac{2}{3}\left(9- t ^{2}\right)\). The value of total heat produced in the coil, till the flux becomes zero, will be \(....J\) 2022 Medium
20. 20. Magnetic flux (in weber) in a closed circuit of resistance \(20\,\Omega\) varies with time \(t(s)\) as \(\phi=8 t ^{2}-9 t +5\). The magnitude of the induced current at \(t =0.25\,s\) will be \(...mA\) 2022 Medium
21. 21. The magnetic flux through a coil perpendicular to its plane is varying according to the relation \(\phi=\) \(\left(5 t^{3}+4 t^2+2 t-5\right) \; Weber\). If the resistant of the coil is \(5 \; ohm\), then the induced current through the coil at \(t =2 \; sec\) will be \(....\,A\) 2022 Medium
22. 22. A circular conducting coil of radius \(1\, {m}\) is being heated by the change of magnetic field \(\vec {B}\) passing perpendicular to the plane in which the coil is laid. The resistance of the coil is \(2\, \mu\, \Omega\). The magnetic field is slowly switched off such that its magnitude changes in time as \(B=\frac{4}{\pi} \times 10^{-3}\, {T}\left(1-\frac{{t}}{100}\right)\) The energy dissipated by the coil before the magnetic field is switched off completely is \(E=.....\,{m} J.\) 2021 Medium
23. 23. A coil is placed in a magnetic field \(\overrightarrow{{B}}\) as shown below: A current is induced in the coil because \(\overrightarrow{{B}}\) is:
    2021 Medium
24. 24. In the given figure the magnetic flux through the loop increases according to the relation \(\phi_{B}(t)=10 t^{2}+20 t\), where \(\phi_{B}\) is in milliwebers and \(t\) is in seconds. The magnitude of current through \({R}=2 \,\Omega\) resistor at \({t}=5\, {s}\) is \(....\,{mA}\).
    2021 Medium
25. 25. A long solenoid of radius \(\mathrm{R}\) carries a time \((t)-\)dependent current \(\mathrm{I}(\mathrm{t})=\mathrm{I}_{0} \mathrm{t}(1-\mathrm{t})\). A ring of radius \(2 \mathrm{R}\) is placed coaxially near its middle. During the time interval \(0 \leq t \leq 1\), the induced current \(\left(\mathrm{I}_{\mathrm{R}}\right)\) and the induced \(\mathrm{EMF}\left(\mathrm{V}_{\mathrm{R}}\right)\) in the ring change as 2020 Hard
26. 26. A planar loop made of wire is rotating in a uniform magnetic field. At time \(t=0\), the plane of the loop is perpendicular to the magnetic field. If the loop is rotating about an axis passing through its plane with a period of \(10\) seconds, at which of the following times will the induced electromotive force (emf) be maximum and minimum, respectively? 2020 Hard
27. 27. 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 \(100 p\) is close to \(....A\) (Resistivity of the metal wire is \(\left.1.23 \times 10^{-8}\, \Omega m \right)\) 2020 Hard
28. 28. At time \(\mathrm{t}=0\) 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 \(5 \;\mathrm{s}\), then induced \(EMF\) in the loop is ........\( \mu \mathrm{V}\)
    2020 Medium
29. 29. Two concentric circular coils, \(C _{1}\) and \(C _{2}\), are placed in the \(XY\) plane. \(C _{1}\) has \(500\) turns, and a radius of \(1\; cm . C _{2}\) has \(200\) turns and radius of \(20\, cm . C _{2}\) carries a time dependent current \(I(t)=\left(5 t^{2}-2 t+3\right) \;A\) where \(t\) is in \(s\). The \(emf\) nduced in \(C _{1}\) (in \(mV\) ), at the instant \(t =1\; s\) is \(\frac{4}{ x }\). The value of \(x\) is 2020 Medium
30. 30. A conducting circular loop made of a thin wire, has area \(3.5 \times 10^{-3}\, m^2\) and resistance \(10\,\Omega \). It is placed perpendicular to a time dependent magnetic field \(B(t) = (0.4\,T)\, sin\, (50\, \pi t)\). The field is uniform in space. Then the net charge flowing through the loop during \(t = 0\, s\) and \(t = 10\, ms\) is close to.......\(mC\) 2019 Hard
31. 31. In a coil of resistance \(100\ \Omega\) , a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is......\(Wb\)
    2017 Medium

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