Ampere's Law and Displacement Current

Practice Questions:

Question 1: easy

To produce an instantaneous displacement current of 2 mA in the space between the parallel plates of a capacitor of capacitance 4 \(\mu\)F, the rate of change of applied variable potential difference \(\left(\frac{dV}{dt}\right)\) must be

1. 200 V/s

2. 400 V/s

3. 800 V/s

4. 500 V/s

View Answer

Displacement current is given by \(I_d = C \frac{dV}{dt}\). Substituting the values: \(2 \times 10^{-3} = 4 \times 10^{-6} \frac{dV}{dt} ⇒ \frac{dV}{dt} = 500\text{ V/s}\).

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Question 2: easy

Displacement current is same as:

1. conduction current due to flow of free electron

2. conduction current due to flow of positive ions

3. conduction current due to flow of both positive and negative free charge carriers

4. is not a conduction current but is caused by time varying electric field

View Answer

Displacement current represents the rate of change of electric displacement field and is not caused by real movement of charges like conduction current.

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Question 3: easy

The potential difference between the plates of a parallel plate capacitor is changing at the rate of \(10^6\text{ V/s}\). If the capacitance is \(2\ \mu\text{F}\), the displacement current in the dielectric of the capacitor will be:

1. \(1\text{ A}\)

2. \(2\text{ A}\)

3. \(3\text{ A}\)

4. \(4\text{ A}\)

View Answer

Displacement current is given by \(I_d = C \frac{dV}{dt}\). Substituting \(C = 2 \times 10^{-6}\text{ F}\) and \(\frac{dV}{dt} = 10^6\text{ V/s}\), we find \(I_d = 2\text{ A}\).

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Question 4: easy

Modified ampere circuital law is given by (symbols have their usual meaning)

1. \(\oint \vec{B} \cdot d\vec{l} = 0\)

2. \(\oint \vec{B} \cdot d\vec{l} = \mu_0 I_C\)

3. \(\oint \vec{B} \cdot d\vec{l} = \mu_0(I_C + I_D)\)

4. \(\oint \vec{B} \cdot d\vec{l} = \mu_0 I_D\)

View Answer

The generalized Ampere's circuital law (or Ampere-Maxwell law) includes both conduction current \(I_C\) and displacement current \(I_D\) as sources of magnetic fields, expressed as \(\oint \vec{B} \cdot d\vec{l} = \mu_0(I_C + I_D)\).

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Question 5: easy

A capacitor of capacitance \(C\), is connected across an ac source of voltage \(V\), given by \(V = V_0\sin\omega t\). The displacement current between the plates of the capacitor, would then be given by

1. \(I_d = V_0\omega C\sin\omega t\)

2. \(I_d = V_0\omega C\cos\omega t\)

3. \(I_d = \frac{V_0}{\omega C}\cos \omega t\)

4. \(I_d = \frac{V_0}{\omega C}\sin \omega t\)

View Answer

The displacement current is equal to the conduction current, which is \(I_d = \frac{dq}{dt}\). Since \(q = CV = C V_0 \sin\omega t\), differentiating with respect to time gives \(I_d = V_0 \omega C \cos\omega t\).

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Question 6: easy

Displacement current exists within the gap between the plates of capacitor when the electric field between its plates

1. Increases with time

2. Decreases with time

3. Remains constant

4. Both (1) and (2)

View Answer

Displacement current is given by \(I_d = \varepsilon_0 \frac{d\Phi_E}{dt}\). It exists whenever there is a changing electric field, whether it increases or decreases with time.

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Question 7: easy

Displacement current exists within the gap between the plates of capacitor when the electric field between its plates

1. Increases with time

2. Decreases with time

3. Remains constant

4. Both (1) and (2)

View Answer

Displacement current is given by \(I_d = \varepsilon_0 \frac{d\Phi_E}{dt}\). Hence, it exists whenever the electric field changes (increases or decreases) with time.

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Question 8: easy

Assertion (A): Conduction and displacement current may be present in the same region of space.

Reason (R): There is no perfectly conducting or perfectly insulating medium.

1. Both (A) \(&\) (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) \(&\) (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

In a real dielectric medium with some conductivity, both conduction current (due to charge movement) and displacement current (due to changing electric fields) can exist simultaneously. As no material is perfectly conducting or insulating, this coexistence is possible.

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Question 9: easy

Assertion (A): A magnetic needle when placed in between the plates of a parallel plate capacitor under charging, the needle shows deflection.

Reason (R):As the charge on the capacitor plates increases, the electric field and the electric flux between the plates changes which generates a magnetic field.

1. Both (A) &(R) are true and the (R) is the correct explanation of the (A)

2. Both (A) &(R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

During capacitor charging, the changing electric field produces a displacement current \(I_d = epsilon_0 frac{dPhi_E}{dt}\). This displacement current generates a magnetic field, causing the needle to deflect. Thus, A and R are true, and R explains A.

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Question 10: moderate

To produce an instantaneous displacement current of 2 mA in the space between the parallel plates of a capacitor of capacitance \(4 \mu\text{F}\), the rate of change of applied variable potential difference \(\left(\frac{dV}{dt}\right)\) must be

1. 200 V/s

2. 400 V/s

3. 800 V/s

4. 500 V/s

View Answer

Since displacement current is given by \(I_d = C \frac{dV}{dt}\), we find \(\frac{dV}{dt} = \frac{I_d}{C} = \frac{2 \times 10^{-3} \text{A}}{4 \times 10^{-6} \text{F}} = 500 \text{V/s}\).

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