Read the following passage and answer the questions.
A parallel plate capacitor has two plates, each of area 0.10 m2, with air between them. A source charges the capacitor. The current in the connecting wires stays constant at 0.885 mA. Take \(\varepsilon_0=8.85\times10^{-12}\ \mathrm{C^{2}\,N^{-1}\,m^{-2}}\). A student draws a circular loop of radius \(r\) around one connecting wire, close to a plate. The plane of the loop is perpendicular to the wire. She marks a point P on the loop. She wants to find the magnetic field at P with the help of Ampere’s law. For this, she takes two surfaces that have the loop as their rim (edge). The first is a flat circular disc, and the wire passes through it. The second is a pot-shaped surface. Its bottom lies in the gap between the plates, and it does not touch the wire anywhere.
Consider the following statements:
(A) The displacement current has the same physical effects as the conduction current.
(B) Charges moving with a uniform velocity radiate electromagnetic waves.
(C) The total current is the sum of the conduction current and the displacement current.
(D) Faraday’s law states that the induced emf is equal to the rate of change of electric flux.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) and (C) only
Maxwell added a second term to Ampere’s law. This displacement current, \( i_d=\varepsilon_0\,d\Phi_E/dt \), comes from an electric field that changes with time.
(A) The displacement current has the same physical effects as the conduction current. — True. It is a source of magnetic field in the same way as the conduction current.
(B) Charges moving with a uniform velocity radiate electromagnetic waves. — False. Charges in uniform motion form a steady current, and its magnetic field does not change with time. Only accelerated charges radiate electromagnetic waves.
(C) The total current is the sum of the conduction current and the displacement current. — True. This is the total current \( i=i_c+i_d \) used in the Ampere-Maxwell law.
(D) Faraday’s law states that the induced emf is equal to the rate of change of electric flux. — False. Faraday’s law links the induced emf to the rate of change of magnetic flux. A changing electric flux gives the displacement current instead.
NCERT (2026-27):
Displacement Current – “In all respects, the displacement current has the same physical effects as the conduction current. …”
Sources of electromagnetic waves – “Neither stationary charges nor charges in uniform motion (steady currents) can be sources of electromagnetic waves.”
Displacement Current – “More precisely, the total current i is the sum of the conduction current denoted by ic, and the displacement current denoted by id (= ε0 (dΦE/dt)). So we have”
\( \displaystyle i=i_c+i_d \)\( \displaystyle =i_c+\varepsilon_0\frac{d\Phi_E}{dt} \qquad (8.5) \)
Displacement Current – “Faraday’s law of induction states that there is an induced emf equal to the rate of change of magnetic flux.”