Identify the incorrect statements among the following.
A. The displacement current flows in a dielectric of capacitor when the potential difference across its plates is decreasing with time.
B. The direction of propagation of electromagnetic waves is given by \( \vec{E} \times \vec{B} \)
C. The dimensions of \( \varepsilon_0 \displaystyle\frac{d\Phi_E}{dt} \) are the same as that of electric voltage.
D. The amplitudes of electric field and magnetic field are same in an electromagnetic wave.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → C and D only
The displacement current is \( I_d = \varepsilon_0\,d\Phi_E/dt \); in an electromagnetic wave E and B are perpendicular, oscillate in phase and have amplitudes related by \( E_0 = cB_0 \).
(A) The displacement current flows in a dielectric of capacitor when the potential difference across its plates is decreasing with time. — Correct statement. A displacement current exists whenever the electric field between the plates changes, whether the potential difference is rising or falling.
(B) The direction of propagation of electromagnetic waves is given by \( \vec{E} \times \vec{B} \) — Correct statement. The wave travels along \( \vec{E} \times \vec{B} \), the direction in which it carries energy.
(C) The dimensions of \( \varepsilon_0 \displaystyle\frac{d\Phi_E}{dt} \) are the same as that of electric voltage. — Incorrect statement. This quantity is the displacement current, so it has the dimensions of current, not voltage.
\( [\varepsilon_0\,d\Phi_E/dt] = [I_d] = [\mathrm{A}] \)
(D) The amplitudes of electric field and magnetic field are same in an electromagnetic wave. — Incorrect statement. The amplitudes are related by the speed of light, so in SI units \( E_0 \) is \( 3\times10^{8} \) times \( B_0 \).
\( E_0 = cB_0 \)
NCERT (2026-27):
Summary – “1. Maxwell found an inconsistency in the Ampere’s law and suggested the existence of an additional current, called displacement current, to remove this inconsistency. This displacement current is due to time-varying electric field and is given by
\( \displaystyle i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \)
and acts as a source of magnetic field in exactly the same way as conduction current.”
Summary – “… 4. Electric and magnetic fields oscillate sinusoidally in space and time in an electromagnetic wave. The oscillating electric and magnetic fields, E and B are perpendicular to each other, and to the direction of propagation of the electromagnetic wave.”
Summary – “… They are related by
\( \displaystyle E_0/B_0 = c \)”