Displacement Current - UNSOLVED PRACTICE SET
Chapter: Electromagnetic Waves | Topic: Displacement Current
DISPLACEMENT CURRENT - UNSOLVED PRACTICE SET
Topic: Displacement Current
Multiple Choice Questions
Q1. Displacement current is defined as:
- The current due to flow of charges in a conductor
- The rate of change of electric flux through a surface
- The current in a dielectric material only
- The magnetic field produced by moving charges
Q2. The displacement current was introduced by Maxwell to:
- Explain Ohm's law
- Remove the inconsistency in Ampere's circuital law
- Explain electromagnetic induction
- Describe the photoelectric effect
Q3. Displacement current exists:
- Only in conductors
- Only in vacuum
- Both in vacuum and in dielectrics
- Only in magnetic materials
Q4. The magnitude of displacement current is given by:
- I_d = ε₀ dΦ_E/dt
- I_d = dΦ_E/dt
- I_d = ε₀ Φ_E
- I_d = Φ_E/ε₀
Q5. During the charging of a parallel plate capacitor, the displacement current in the region between the plates:
- Is zero
- Is equal to the conduction current in the connecting wires
- Is greater than the conduction current
- Is opposite to the conduction current
Q6. The displacement current density is given by:
- J_d = ε₀ dE/dt
- J_d = dE/dt
- J_d = ε₀ E
- J_d = E/ε₀
Short Answer Questions
Q7. What is displacement current? How does it differ from conduction current?
Q8. Why did Maxwell introduce the concept of displacement current? What inconsistency did it resolve in Ampere's circuital law?
Q9. A parallel plate capacitor is being charged by a battery. Is there a displacement current between the plates? Explain.
Q10. Write the modified Ampere-Maxwell law. Explain the significance of each term.
Q11. Why is displacement current called a 'current' even though no actual charge flows between the capacitor plates?
Q12. Show that the displacement current between the plates of a charging capacitor is equal to the conduction current in the external circuit.
Long Answer Questions
Q13. Explain the concept of displacement current with a suitable example. Show that displacement current arises due to the time-varying electric field and derive its expression.
Q14. Describe the process of charging a parallel plate capacitor and explain how displacement current flows between the plates. Show mathematically that I_d = I_c (conduction current) at every instant.
Q15. Discuss the physical significance of displacement current. How did it lead to the prediction of electromagnetic waves? Explain the symmetry it introduced in Maxwell's equations.
Numerical & Application-Based Problems
Q16. A parallel plate capacitor with plate area 2 × 10⁻³ m² and plate separation 1 mm is connected to a 100 V battery through a resistor. The electric field between the plates changes at a rate of 10¹⁰ V/m·s.
(a) Calculate the displacement current between the plates.
(b) Calculate the conduction current in the connecting wire.
(c) Determine the rate of change of charge on the plates.
Q17. The electric field between the plates of a parallel plate capacitor is given by E = (2 × 10⁵ t) V/m, where t is in seconds. The area of each plate is 0.05 m².
(a) Calculate the displacement current density.
(b) Calculate the total displacement current between the plates.
(c) If the capacitor is connected to a circuit, what is the conduction current in the wires?
Q18. In your school's physics lab, a student sets up an experiment with a parallel plate capacitor connected to an AC source of frequency 50 Hz. The peak voltage is 10 V, the plate area is 100 cm², and the plate separation is 2 mm.
(a) Calculate the maximum value of the displacement current between the plates.
(b) Write the expression for the displacement current as a function of time.
(c) At what instant during the cycle is the displacement current maximum? At what instant is it zero?
(d) A classmate argues that since no charge actually crosses the gap between the plates, the term 'displacement current' is misleading. Present your argument for why Maxwell chose this term and why it is physically meaningful.