Physics Class 12 NCERT Solutions: Chapter 8 Electromagnetic Waves Part 1

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Charging Progresses

Charging Progresses

Charging Progresses

Q: 1. Figure shows a capacitor made of two circular plates each of radius , and separated by . The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to .

(A) Calculate the capacitance and the rate of charge of potential difference between the plates.

(B) Obtain the displacement current across the plates.

(C) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

Q 1 Image of Two Circular Plates

Q 1 Image of Two Circular Plates

Q 1 Image of Two Circular Plates

Answer:

Radius of each circular plate,

Distance between the plates,

Charging current,

Permittivity of free space,

(A) Capacitance between the two plates is given by the relation,

Where,

Charge on each plate,

Where,

Potential difference across the plates

Differentiation on both sides with respect to time (t) gives:

Therefore, the change in potential difference between the plates is .

(B) The displacement current across the plates is the same as the conduction current.

Hence, the displacement current, is .

(C) Yes

Kirchhoff’s first rule is valid at each plate of the capacitor provided, that we take the sum of conduction and displacement for current.

Q: 2. A parallel plate capacitor (Figure) made of circular plates each of radius has a capacitance . The capacitor is connected to a supply with a (angular) frequency of .

(A) What is the rms value of the conduction current?

(B) Is the conduction current equal to the displacement current?

(C) Determine the amplitude of B at a point from the axis between the plates.

Q 2 Image of Circular Plate

Q 2 Image of Circular Plates

Q 2 Image of Circular Plate

Answer:

Radius of each circular plate,

Capacitance of a parallel plate capacitor,

Supply voltage,

Angular frequency,

(A) Rms value of conduction current,

Where,

Capacitive reactance

Hence, the rms value of conduction current is .

(B) Yes, conduction current is equal to displacement current.

(C) Magnetic field is given as:

Where,

Free space permeability

Distance between the plates from the axis

Hence, the magnetic field at that point is .

Q: 3. What physical quantity is the same for of wavelength , red light of wavelength and radio waves of wavelength ?

Answer

The speed of light in a vacuum is the same for all wavelengths. It is independent of the wavelength in the vacuum.