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.
While the capacitor is being charged, the rate at which the electric field between its plates increases is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(1.0\times10^{9}\ \mathrm{V\,m^{-1}\,s^{-1}}\)
Between the plates, the electric field is \( E=Q/\varepsilon_0A \). The charge on the plates grows at the rate \( dQ/dt=i \), so the field grows at the rate \( i/\varepsilon_0A \).
Given:
\( A=0.10\ \mathrm{m^{2}} \)
\( i=0.885\ \mathrm{mA}=0.885\times10^{-3}\ \mathrm{A} \)
\( \varepsilon_0=8.85\times10^{-12}\ \mathrm{C^{2}\,N^{-1}\,m^{-2}} \)
\( \begin{aligned} \frac{dE}{dt} &= \frac{1}{\varepsilon_0A}\frac{dQ}{dt} \\ &= \frac{i}{\varepsilon_0A} \\ &= \frac{0.885\times10^{-3}}{8.85\times10^{-12}\times0.10} \\ &= \frac{0.885\times10^{-3}}{8.85\times10^{-13}} \\ &= 1.0\times10^{9}\ \mathrm{V\,m^{-1}\,s^{-1}} \end{aligned} \)
Therefore, the field between the plates rises by \( 1.0\times10^{9}\ \mathrm{V\,m^{-1}} \) every second.
NCERT (2026-27):
Displacement Current – “If the plates of the capacitor have an area A, and a total charge Q, the magnitude of the electric field E between the plates is (Q/A)/ε0 … Now if the charge Q on the capacitor plates changes with time, there is a current i = (dQ/dt), …”