Physics Questions and Answers – Displacement Current

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This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Displacement Current”.

1. Which one of the following current flows in the gap between the capacitor plates?
a) Displacement current
b) Conduction current
c) Resistive current
d) Total current

Explanation: Displacement current (ID) is the electric current that flows in the gap between the plates of the capacitor during its charging, which originates due to the time-varying electric field in the space between the two plates of the capacitor. The expression for displacement current is given as:
ID = εo $$\frac {d\Phi_{\varepsilon}}{dt}$$

2. Identify the expression of Ampere-Maxwell’s Circuital law.
a) ∮$$\overset{\rightharpoonup}{B}.\overset{\rightharpoonup}{dl}$$ = μ0 (IC-ID)
b) ∮$$\overset{\rightharpoonup}{B}.\overset{\rightharpoonup}{dl}$$ = μ0 (ID-IC)
c) ∮$$\overset{\rightharpoonup}{B}.\overset{\rightharpoonup}{dl}$$ = μ0 (IC+ID)
d) ∮$$\overset{\rightharpoonup}{B}.\overset{\rightharpoonup}{dl}$$ = μ0 (IC ID)

Explanation: The Ampere-Maxwell Law tells you that this quantity is proportional to the enclosed current and rate of change of electric flux through any surface bounded by the path of integration. The expression for Ampere-Maxwell’s law is given as:
∮$$\overset{\rightharpoonup}{B}.\overset{\rightharpoonup}{dl}$$ = μ0(IC+ID)

3. Find the true statement.
a) Displacement current and conduction current are never equal
b) The current that flows through connection wires is called conduction current
c) During charging of the capacitor, in the connection wires, conduction current is discontinuous and displacement current is continuous
d) During charging of the capacitor, in the gap between the capacitor plates, conduction current is continuous and displacement current is discontinuous

Explanation: The true statement is ➔ the current that flows through the connection wires is called conduction current. All the other statements are not valid. Displacement current and conduction current can numerically be equal. During charging of the capacitor, in the connection wires, conduction current is continuous and displacement current is discontinuous. Similarly, during the charging of the capacitor, in the gap between the capacitor plates, conduction current is discontinuous and the displacement current is continuous.

4. Maxwell modified Ampere’s Circuital Law.
a) True
b) False

Explanation: Yes, Maxwell modified Ampere’s Law. Ampere’s law is true just for steady currents. Maxwell found the shortcoming in Ampere’s law and he modified Ampere’s law to incorporate time-varying electric fields. Maxwell was the one responsible for the correction of the Ampere’s circuital law by the addition of displacement current. He said that we’ve to think about not only the present existing outside the capacitor but also the present referred to as displacement current that existed between the plates of the capacitor.

5. A parallel plate capacitor with plate area A and separation between the plates d, is charged by a constant current I. Consider a plane surface of area A/4 parallel to the plates and drawn between the plates. What is the displacement current through this area?
a) I
b) $$\frac {I}{4}$$
c) 4I
d) $$\frac {I}{2}$$

Explanation: Electric field between the plates is given as:
E=$$\frac {q}{A\varepsilon_o}=\frac {It}{A\varepsilon_o}$$
So, the electric flux through the area $$\frac {A}{4}$$ is given by:
ΦE=$$(\frac {A}{4})$$E=$$\frac {It}{4\varepsilon_o}$$
Then the displacement current will be:
ID = εo$$\frac {d\Phi_E}{dt}$$
ID = εo$$\frac {d}{dt} (\frac {It}{4\epsilon_o})=\frac {I}{4}$$
Therefore, the displacement current through this area is $$\frac {I}{4}$$.