A capacitor consists of two concentric conducting spherical surfaces of radii a and b (a < b) and charge of Q. The medium between the conductors has a dielectric constant (relative permittivity) of &, =where R is the radial distance. R a) Using Gauss' law find the electric field intensity E between the plates. b) Find the electric potential difference between the conductors. c) What is the capacitance? d) Find the energy stored in the capacitor in two ways (your results should match): • Using capacitance found in part (c) based on W. =; Q²/C. 1 • Using the energy density we the capacitor. ɛE² and integrating over the entire volume of

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A capacitor consists of two concentric conducting spherical surfaces of radii a and b (a < b)
and charge of Q. The medium between the conductors has a dielectric constant (relative
1
permittivity) of ɛ, = where R is the radial distance.
R
a) Using Gauss' law find the electric field intensity Ē between the plates.
b) Find the electric potential difference between the conductors.
c) What is the capacitance?
d) Find the energy stored in the capacitor in two ways (your results should match):
• Using capacitance found in part (c) based on W. = Q²/C.
2
1
Using the energy density we = ɛE? and integrating over the entire volume of
the capacitor.
2
Transcribed Image Text:A capacitor consists of two concentric conducting spherical surfaces of radii a and b (a < b) and charge of Q. The medium between the conductors has a dielectric constant (relative 1 permittivity) of ɛ, = where R is the radial distance. R a) Using Gauss' law find the electric field intensity Ē between the plates. b) Find the electric potential difference between the conductors. c) What is the capacitance? d) Find the energy stored in the capacitor in two ways (your results should match): • Using capacitance found in part (c) based on W. = Q²/C. 2 1 Using the energy density we = ɛE? and integrating over the entire volume of the capacitor. 2
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