Motional EMF - UNSOLVED PRACTICE SET

Q7. Derive the expression for motional EMF: ε = Blv. Explain the physical meaning of each term.

Q8. A rod of length 40 cm moves perpendicular to a magnetic field of 0.5 T with speed 10 m/s. Calculate the motional EMF.

Q9. Explain motional EMF using the concept of Lorentz force on charge carriers in the moving conductor.

Q10. A conducting rod moves on parallel rails in a magnetic field. What is the direction of induced current? Use Fleming's right-hand rule.

Q11. Why does a conductor moving in a magnetic field experience a magnetic force opposing its motion? Explain using Lenz's Law.

Q12. A circular metal disc of radius 20 cm rotates at 10 rev/s in a magnetic field of 0.3 T perpendicular to the disc. Calculate the EMF between the center and the rim.

Q13. Derive the expression for motional EMF in a straight conductor moving perpendicular to a uniform magnetic field. Explain using both (a) Faraday's law (flux cutting), and (b) Lorentz force on charge carriers. Show that both approaches give the same result.

Q14. A conducting rod of length l rotates with angular velocity ω about one end in a uniform magnetic field B perpendicular to the plane of rotation. Derive the expression for the EMF induced between the center and the free end. Why is the factor ½ present in the formula?

Q15. A rod of length l = 60 cm and mass m = 100 g rests on two parallel horizontal rails separated by the same distance. The rails are connected by a resistor R = 3 Ω. A uniform magnetic field B = 0.5 T is applied vertically downward. The rod is given an initial velocity v₀ = 8 m/s.

(a) Calculate the initial induced EMF.

(b) Calculate the initial induced current.

(c) Calculate the magnetic force on the rod.

(d) Describe the subsequent motion of the rod.

(e) Calculate the distance traveled before the rod stops.

[Given: g = 9.8 m/s²]

Q6. In a school physics lab, a student sets up a "rail gun" demonstration. Two parallel copper rails are 20 cm apart, connected at one end by a resistor R = 5 Ω. A conducting rod of mass m = 50 g can slide on the rails. A uniform magnetic field B = 0.6 T is applied vertically upward.

(a) The rod is pulled with constant force F = 0.5 N. Calculate the initial acceleration.

(b) As the rod moves, calculate the induced EMF and current when its speed is 5 m/s.

(c) Calculate the magnetic force opposing the motion at this speed.

(d) Find the terminal velocity of the rod (when applied force equals magnetic force).

(e) Calculate the power supplied by the external force and the power dissipated in the resistor at terminal velocity. Verify they are equal.

[Given: g = 9.8 m/s²]

Q17. An electric generator in a small hydroelectric plant uses a rotating copper disc (Faraday disc) of radius R = 50 cm rotating at 300 rpm in a magnetic field B = 0.4 T perpendicular to the disc.

(a) Calculate the angular velocity in rad/s.

(b) Calculate the EMF between the center and the rim of the disc.

(c) If the disc has resistance 0.01 Ω and is connected to a load of 10 Ω, calculate the current and power delivered.

(d) Calculate the torque required to maintain the rotation at constant speed.

(e) Explain why Faraday disc generators are not commonly used today despite their simplicity.

Q18. A rectangular conducting loop with sides a = 25 cm and b = 40 cm is pulled out of a region of uniform magnetic field B = 0.8 T (perpendicular to the loop) with constant velocity v = 2 m/s. The loop has resistance R = 4 Ω and mass m = 200 g.

(a) Calculate the induced EMF while the loop is being pulled out.

(b) Calculate the induced current and its direction.

(c) Calculate the magnetic force opposing the motion.

(d) Calculate the power required to pull the loop at constant velocity.

(e) If the pulling force is removed, calculate the initial deceleration of the loop.

(f) Verify that the mechanical work done equals the electrical energy dissipated.