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Worksheet: Capacitance of a Spherical Capacitor

Q1:

A spherical capacitor is formed from two concentric spherical conducting spheres separated by vacuum. The inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor.

What is the capacitance of the capacitor?

What is the magnitude of the electrical field at , just outside the inner sphere?

What is the magnitude of the electrical field at , just inside the outer sphere?

Q2:

Earth can be considered as a spherical capacitor with two plates, where the negative plate is the surface of Earth and the positive plate is the bottom of the ionosphere, which is located at an altitude of approximately 70 km. The potential difference between Earth’s surface and the ionosphere is about V.

Calculate the capacitance of this system.

Find the total charge on this capacitor.

Find the energy stored in this system.

Q3:

Consider Mars to be a spherical conductor of radius 3 400 km. What is its capacitance?

Q4:

A capacitor is made from two concentric spheres; one with radius 8.00 cm and the other with radius 7.00 cm, with vacuum between them.

What is the capacitance of this set of conductors?

If the region between the conductors is filled with a material whose dielectric constant is 5.00, what is the capacitance of the system?

Q5:

What is the capacitance of a large Van de Graaff generator’s terminal given that it stores 5.00 mC of charge at a voltage of 6.0 MV?