Question

A parallel plate capacitor with circular plates of radius R = 16.0 cm and plate separation d = 9.00 mm is being charged at the rate of 8.00 C/s.

What is the displacement current through a circular loop of radius r = 21.00 cm centered on the axis of the capacitor? 8.00 You are correct.

What is the displacement current through a circular loop of radius r = 3.00 cm centered on the axis of the capacitor?

What is the magnitude of the magnetic field between the capacitor plates at a radius r = 3.00 cm from the axis of the capacitor?

Answer 1

Concepts and reason

The concept used to solve this problem is the displacement current and Biot-Savart law.

Initially, use the rate of charge and radius of circular plates to calculate the displacement current when the radius of circular loop is .

Then, use rate of charge, radius of circular plates, and radius of circular loop to calculate the displacement current.

Finally, use the displacement current, permeability of free space, and the radius of circular loop to calculate the magnetic field between the capacitor plates.

Fundamentals

The current that flows between the plates is known as the displacement current. Due to the displacement current, the magnetic field is formed between the parallel plates of the capacitor.

The formula to calculate the displacement current is given below:

Here, is the rate of charge, is the radius of circular plates, is the displacement current, and is the radius of circular loop.

According to the Biot-Savart law,

The magnitude of the magnetic field depends on the amount of current and the distance from the current-carrying wire.

The expression for the magnetic field is given below:

Here, is the permeability of free space and magnetic field is .

The formula to calculate the displacement current is given below:

Since, , the common area is the smaller area.

Therefore,

The above expression becomes as follows:

Substitute for , and for .

The formula to calculate the displacement current is given below:

Since, consider both the radii.

Substitute for , for and for .

The expression for the magnetic field is given below:

Substitute for , for and for .

Ans:

Thus, the displacement currents are and respectively, and the magnetic field is .