Motional EMF (Induced Parameter) PYQs: JEE Mains Physics

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1. 1. A metal rod of length \(L\) rotates about one end at origin with a uniform angular velocity \(\omega\). The magnetic field radially falls off as \(B(r) = B_0 e^{-\lambda r}\); \(\lambda\) being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is : 2026 Hard
2. 2. Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current \(I=10 \sin (\omega t ) A\), where \(\omega=1000 rad . / s\). A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed \(v =1 cm / s\). The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is \(\alpha / \sqrt{2} \quad \mu A\). The value of \(\alpha\) is ___________.
   [Resistance of the loop \(=10 \Omega\) ] 2026 Hard
3. 3.
   A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time \(t=0\) with a constant velocity. If the induced EMF is \(\mathrm{E} \propto \mathrm{t}^{\mathrm{n}}\), then value of n is ________. 2025 Medium
4. 4. A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of \(10 \pi \mathrm{rad} \mathrm{s}^{-1}\) about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim ? \((\pi=3.14)\) 2025 Medium
5. 5. Conductor wire ABCDE with each \(\operatorname{arm} 10 \mathrm{~cm}\) in length is placed in magnetic field of \(\frac{1}{\sqrt{2}}\) Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of \(10 \mathrm{~cm} / \mathrm{s}\), induced emf between points A and E is _____ mV.
   2025 Hard
6. 6. A ceiling fan having 3 blades of length \(80 \mathrm{~cm}\) each is rotating with an angular velocity of \(1200\  \mathrm{rpm}\). The magnetic field of earth in that region is \(0.5 \ \mathrm{G}\) and angle of dip is \(30^{\circ}\). The emf induced across the blades is \(N \pi \times 10^{-5} \mathrm{~V}\). The value of \(\mathrm{N}\) is _______. 2024 Hard
7. 7. A horizontal straight wire \(5 \mathrm{~m}\) long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field \(0.60 \times 10^{-4} \ \mathrm{Wbm}^{-2}\). The instantaneous value of emf induced in the wire when its velocity is \(10 \mathrm{~ms}^{-1}\) is _______ \(\times 10^{-3} \mathrm{~V}\) 2024 Hard
8. 8. A rectangular loop of length \(2.5 \mathrm{~m}\) and width \(2 \mathrm{~m}\) is placed at \(60^{\circ}\) to a magnetic field of \(4 \mathrm{~T}\). The loop is removed from the field in \(10 \ \mathrm{sec}\). The average emf induced in the loop during this time is 2024 Hard
9. 9. A rectangular loop of sides \(12 \mathrm{~cm}\) and \(5 \mathrm{~cm}\), with its sides parallel to the \(x\)-axis and \(y\)-axis respectively moves with a velocity of \(5 \mathrm{~cm} / \mathrm{s}\) in the positive \(\mathrm{x}\) axis direction, in a space containing a variable magnetic field in the positive \(z\) direction. The field has a gradient of \(10^{-3} \mathrm{~T} / \mathrm{cm}\) along the negative \(\mathrm{x}\) direction and it is decreasing with time at the rate of \(10^{-5} \mathrm{~T} / \mathrm{s}\). If the resistance of the loop is \(6 \mathrm{~m} \Omega\), the power dissipated by the loop as heat is _______ \(\times 10^{-9} \mathrm{~W}\). 2024 Hard
10. 10. A rod of length \(60 \mathrm{~cm}\) rotates with a uniform angular velocity \(20 \mathrm{rad} \mathrm{s}^{-1}\) about its perpendicular bisector, in a uniform magnetic field \(0.5 \mathrm{~T}\). The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is________\(V\). 2024 Hard
11. 11. A square loop of side \(15 \mathrm{~cm}\) being moved towards right at a constant speed of \(2 \mathrm{~cm} / \mathrm{s}\) as shown in figure. The front edge enters the \(50 \mathrm{~cm}\) wide magnetic field at \(t=0\). The value of induced emf in the loop at \(t=10 \mathrm{~s}\) will be _______.
    2024 Hard
12. 12. A square loop \(\mathrm{PQRS}\) having \(10\) turns, area \(3.6 \times\) \(10^{-3} \mathrm{~m}^2\) and resistance \(100 \Omega\) is slowly and uniformly being pulled out of a uniform magnetic field of magnitude \(\mathrm{B}=0.5 \mathrm{~T}\) as shown. Work done in pulling the loop out of the field in \(1.0 \mathrm{~s}\) is _______ \(\times 10^{-6} \mathrm{~J}\).
    2024 Hard
13. 13. A \(1\,m\) long metal rod \(XY\) completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \(0.15\,T\). If the resistance of the circuit is \(5\,\Omega\), the force needed to move the rod in direction, as indicated, with a constant speed of \(4\,m / s\) will be \(................\,10^{-3}\,N\)
    2023 Medium
14. 14. A \(20\,cm\) long metallic rod is rotated with \(210\,rpm\) about an axis normal to the rod passing through its one end. The order end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field \(0.2\,T\) parallel to the axis exists everywhere. The emf developed between the centre and the ring is \(.......\,mV\).Take \(\pi=\frac{22}{7}\) 2023 Medium
15. 15. A wire of length \(1\,m\) moving with velocity \(8\,m / s\) at right angles to a magnetic field of \(2\,T\). The magnitude of induced emf, between the ends of wire will be \(............\,V\) 2023 Easy
16. 16. An \(emf\) of \(0.08\,V\) is induced in a metal rod of length \(10\,cm\) held normal to a uniform magnetic field of \(0.4\,T\), when moves with a velocity of ...........\(ms^{-1}\) 2023 Medium
17. 17. The induced \(emf\) can be produced in a coil by \(A.\) moving the coil with uniform speed inside magnetic field \(B.\) moving the coil with non-uniform speed inside uniform magnetic field \(C.\) rotating the coil inside the uniform magnetic field \(D.\) changing the area of the coil inside the uniform magnetic field Choose the correct answer from the options given below: 2023 Medium
18. 18. A metallic conductor of length \(1\; m\) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \(5 \;rad / s\). If the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \;T\), then emf induced between the two ends of the conductor is ............. 2022 Medium
19. 19. A constant magnetic field of \(1 \,{T}\) is applied in the \({x}\,>\,0\) region. A metallic circular ring of radius \(1 \,{m}\) is moving with a constant velocity of \(1 \,{m} / {s}\) along the \(x\)-axis. At \(t=0\) \(s,\) the centre of \(O\) of the ring is at \({x}=-1 \,{m}\). What will be the value of the induced \(emf\) in the ring at \(t=1\, s\) ? (Assume the velocity of the ring does not change.) (In \({V}\))
    2021 Hard
20. 20. A square loop of side \(20\, {cm}\) and resistance \(1\, \Omega\) is moved towards right with a constant speed \({v}_{0}\). The right arm of the loop is in a uniform magnetic field of \(5\, {T}\). The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value \(4\, \Omega\). What should be the value of \(v_{0}\) so that a steady current of \(2\, {mA}\) flows in the loop ?
    2021 Hard
21. 21. An aeroplane, with its wings spread \(10\, m ,\) is flying at a speed of \(180 \,km / h\) in a horizontal direction. The total intensity of earth's field at that part is \(2.5 \times 10^{-4}\, Wb / m ^{2}\) and the angle of dip is \(60^{\circ}\). The emf induced between the tips of the plane wings will be ...... \(mV\) 2021 Medium
22. 22. The arm \(P Q\) of a rectangular conductor is moving from \(x=0\) to \(x=2 b\) outwards and then inwards from \(x=2 b\) to \(x=0\) as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from \(x=0\) to \(x=b\). Identify the graph showing the variation of different quantities with distance.
    2021 Hard
23. 23. The magnetic field in a region is given by \(\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }\). A square loop of side \(d\) is placed with its edges along the \(x\) and \(y\) axes. The loop is moved with a constant velocity \(\overrightarrow{ v }= v _{0} \hat{ i }\). The emf induced in the loop is:
    2021 Hard
24. 24. 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
    2020 Hard
25. 25. A \(10\,m\) long horizontal wire extends from North East to South West. It is falling with a speed of \(5.0\,ms^{-1},\) at right angles to the horizontal component of the earth’s magnetic field, of \(0.3\times 10^{-4}\,Wb/m^2\). The value of the induced \(emf\) in wire is  2019 Medium
26. 26. A solid metal cube of edge length \(2\, cm\) is moving in a positive \(y-\) direction at a constant speed of \(6\, m/s\). There is a uniform magnetic field of \(0.1\, T\) in the positive \(z-\) direction. The potential difference between the two faces of the cube perpendicular to the \(x-\) axis, is.....\(mV\) 2019 Medium
27. 27. The figure shows a square loop \(L\) of side \(5\, cm\) which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of \(1\, cms^{-1}\). At some instant, a part of \(L\) is in a uniform magnetic field of \(1\, T\), perpendicular to the plane of the loop. If the resistance of \(L\) is \(1.7\,\Omega \), the current in the loop at that instant will be close to.....\(\mu A\)
    2019 Hard
28. 28. A copper rod of mass \(m\) slides under gravity on two smooth parallel rails, with separation \(l\) and set at an angle of \(\theta\) with the horizontal. At the bottom, rails are joined by a resistance \(R\). There is a uniform magnetic field \(B\) normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is
    2018 Hard
29. 29. A square frame of side \(10\, cm\) and a long straight wire carrying current \(1\, A\) are in the plate of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of \(10\, ms^{-1}\) (see figure). The \(e.m. f\) induced at the time the left arm of the frame is at \(x\, = 10\, cm\) from the wire is .....\(\mu V\)
    2014 Medium
30. 30. A metallic rod oflength '\(l\)' is tied to a string oflength \(2l\). and made to rotate with angular speed w on a horizontal table with one end of the string fixed. Ifthere is a vertical magnetic field '\(B\)' in the region, the \(e.m.f.\) induced across the ends of the rod is
    2013 Medium

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