Displacement Current

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

Figure shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A.

1. Calculate the capacitance and the rate of charge of the potential difference between the plates.
2. Obtain the displacement current across the plates.
3. Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

A parallel plate capacitor (Figure) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s⁻¹.

1. What is the rms value of the conduction current?
2. Is the conduction current equal to the displacement current?
3. Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

A capacitor of capacitance ‘C’, is connected across an ac source of voltage V, given by

V = V₀sinωt 

The displacement current between the plates of the capacitor would then be given by:

An electromagnetic wave travelling along z-axis is given as: E = E₀ cos (kz – ωt.). Choose the correct options from the following;

1. The associated magnetic field is given as `B = 1/c hatk xx E = 1/ω (hatk xx E)`.
2. The electromagnetic field can be written in terms of the associated magnetic field as `E = c(B xx hatk)`.
3. `hatk.E = 0, hatk.B` = 0.
4. `hatk xx E = 0, hatk xx B` = 0.

A capacitor of capacitance ‘C’, is connected across an ac source of voltage V, given by V = V₀ sinωt The displacement current between the plates of the capacitor would then be given by ______.

A parallel-plate capacitor of plate-area A and plate separation d is joined to a battery of emf ε and internal resistance R at t = 0. Consider a plane surface of area A/2, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time.

A long straight cable of length `l` is placed symmetrically along z-axis and has radius a(<< l). The cable consists of a thin wire and a co-axial conducting tube. An alternating current I(t) = I₀ sin (2πνt) flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is E(s,t) = µ₀I₀ν cos (2πνt) In `(s/a)hatk`.

1. Calculate the displacement current density inside the cable.
2. Integrate the displacement current density across the cross-section of the cable to find the total displacement current I^d.
3. Compare the conduction current I0 with the displacement current `I_0^d`.