Question C: Consider the following spherical capacitor with inner plate's radius a=1 mm and outer plate's radius is 3 mm. The capacitor has two different dielectric materials as shown in the figure with e1=2.5, E12=3.5.

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Chapter1: Units, Trigonometry. And Vectors
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Question C:
Consider the following spherical capacitor with inner plate's radius a=1 mm and outer plate's radius
is 3 mm. The capacitor has two different dielectric materials as shown in the figure with en=2.5,
E2=3.5.
Material 1
Material 2
Question C-i:
Find the total energy (in pJ) stored in the capacitor when a battery of 7 volts is connected across its
plates.
Hints:
• Derive a formula for the capacitance and use it to calculate the energy.
• Since we have some material (non vacuum), you will need to use the displacement vector
version of Gauss law, not the electric field version.
• You will need to use the boundary conditions at the boundary between the two dielectric
materials.
Question C-ii:
Repeat assuming it is a cylindrical capacitor with length L=5 cm.
Transcribed Image Text:Question C: Consider the following spherical capacitor with inner plate's radius a=1 mm and outer plate's radius is 3 mm. The capacitor has two different dielectric materials as shown in the figure with en=2.5, E2=3.5. Material 1 Material 2 Question C-i: Find the total energy (in pJ) stored in the capacitor when a battery of 7 volts is connected across its plates. Hints: • Derive a formula for the capacitance and use it to calculate the energy. • Since we have some material (non vacuum), you will need to use the displacement vector version of Gauss law, not the electric field version. • You will need to use the boundary conditions at the boundary between the two dielectric materials. Question C-ii: Repeat assuming it is a cylindrical capacitor with length L=5 cm.
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