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# Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor

A. increases

B. decreases

C. does not change

D. is zero

Answer :

Explanation: The displacement current depends on the changing

electric flux across the capacitor plates. Due to the charging of the

capacitor, the charge varies on the capacitor plates with time. Due

to this, the electric flux also varies with time. The relation between

the displacement current and the electric flux is given as

where *ϕ*_{E} is the time varying electric flux through the plane surface,

ϵ_{0} is the electric permittivity of free space(vacuum) and is equal

to 8.85 × 10^{-12} C^{2} N^{-1} m^{-2} and I_{d} is the displacement current.

The electric flux is given by Gauss’s law as

The displacement current then becomes

which is dependent on charge. If the charge is zero, then the R.H.S

would be zero so D. is incorrect. If the charge doesn’t change with

time so its derivative w.r.t time will be zero and so will be the

current, so C. is zero. For R.H.S to be non-zero, the charge must vary with time i.e. increase or decrease, hence A. and B. are correct.

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Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor

HC Verma - Concepts of Physics Part 2Consider the situation of the previous problem. Define displacement resistance R_{d} = V/i_{d} of the space between the plates where V is the potential difference between the plates and i_{d} is the displacement current. Show that R_{d} varies with time as

R_{d} = R (e^{t/τ} – 1)

HC Verma - Concepts of Physics Part 2

You are given a 2μF parallel plate capacitor. How would you establish an instantaneous displacement current of 1mA in the space between its plates?

Physics - ExemplarUsing B = μ_{0} H find the ratio E_{0}/H_{0} for a plane electromagnetic wave propagating through vacuum. Show that is has the dimensions of electric resistance. This ratio is a universal constant called the impedance of free space.

Show that the dimensions of the displacement current are that of an electric current.

HC Verma - Concepts of Physics Part 2