Lenz's Law - UNSOLVED PRACTICE SET

Q7. State Lenz's Law. How does it embody the principle of conservation of energy?

Q8. A bar magnet's north pole is pushed towards a coil. Predict the direction of induced current in the coil as seen from the magnet side. Explain using Lenz's Law.

Q9. Why does a magnet fall slower through a copper pipe than through a plastic pipe of the same dimensions? Explain using Lenz's Law.

Q10. When a coil carrying current is moved towards a stationary coil, what is the direction of induced current in the stationary coil? Explain.

Q11. A circular loop is pulled out of a region of uniform magnetic field. What is the direction of induced current? Draw a diagram showing the field direction and current direction.

Q12. Explain why Lenz's Law ensures that the induced EMF is always negative in Faraday's law equation.

Q13. State Lenz's Law and explain how it is a consequence of the conservation of energy. Use the example of a magnet being pushed into a coil to illustrate your answer. What would happen if Lenz's Law were opposite?

Q14. Explain the phenomenon of electromagnetic damping using Lenz's Law. How is this principle used in (a) induction cooktops, and (b) eddy current brakes in trains? Draw diagrams showing the directions of induced currents.

Q15. A rectangular conducting loop enters a region of uniform magnetic field B directed into the page with velocity v.

(a) What is the direction of induced current as the loop enters? Explain using Lenz's Law.

(b) What is the direction when the loop is completely inside the field?

(c) What is the direction when the loop exits?

(d) Draw a graph showing the induced current as a function of position as the loop moves through the field.

(e) If the loop is made of insulating material, what happens?

Q16. In a school demonstration, a teacher drops a strong neodymium magnet through a vertical copper tube of length 1 m and inner diameter 2 cm. The magnet takes 2.5 seconds to fall through the tube, compared to 0.45 seconds in free fall.

(a) Calculate the average speed of the magnet through the copper tube.

(b) Explain why the magnet falls slower using Lenz's Law and Faraday's Law.

(c) Calculate the induced EMF in the tube if the magnetic field changes from 0.5 T to 0 at the magnet's average speed.

(d) If the tube is cut lengthwise into a half-cylinder, will the magnet fall faster or slower? Explain.

(e) A student suggests using a superconducting tube (zero resistance). What would happen to the magnet? Explain the phenomenon of magnetic levitation in this context.

Q17. An induction cooktop uses a coil carrying high-frequency alternating current (I = 20 A, f = 25 kHz) placed beneath a copper-bottomed pan. The coil has 20 turns and area 100 cm².

(a) Explain how eddy currents are induced in the pan bottom using Lenz's Law.

(b) Calculate the rate of change of magnetic flux if the field varies sinusoidally.

(c) The pan bottom has resistance 0.01 Ω. Calculate the power dissipated as heat due to eddy currents.

(d) Why does the cooktop not heat up if no pan is placed on it?

(e) Explain why copper-bottomed pans work better than aluminum ones for induction cooking, despite aluminum having lower resistivity.

Q18. A conducting rod of mass m = 200 g and length l = 50 cm slides down frictionless inclined rails that make angle θ = 30° with the horizontal. A uniform magnetic field B = 0.8 T is applied vertically upward. The rails are connected at the bottom by a resistor R = 2 Ω.

(a) Draw the free body diagram for the rod, showing all forces including the magnetic force.

(b) As the rod slides down, what is the direction of induced current? Use Lenz's Law to determine this.

(c) Calculate the terminal velocity of the rod (when magnetic force balances the component of gravity).

(d) Calculate the power dissipated in the resistor at terminal velocity.

(e) Verify that the mechanical power lost (mgv sin θ) equals the electrical power dissipated (I²R), demonstrating conservation of energy.

[Given: g = 9.8 m/s²]