2. A spherical capacitor consists of an inner solid conducting sphere of radius a surrounded by a spherical conducting shell of inner radius b and outer radius e. The capacitor is charged with –Q on the inner sphere and +Q on the outer spherical shell. a) Derive expressions for the electric field everywhere in space due to this charge configuration, indicating both direction and magnitude, in terms of the distance r from the center. Graph the electric field magnitude as a function of r. b) What is the surface charge density on the outer surface of the inner sphere and on the inner surface of the outer sphere? c) In part d) you will calculate the potential difference AV between the inner and outer conductors. Before you calculate the value, indicate what the sign (positive or negative) of AV=Vb – Va must be and give a clear explanation as to why.
2. A spherical capacitor consists of an inner solid conducting sphere of radius a surrounded by a spherical conducting shell of inner radius b and outer radius e. The capacitor is charged with –Q on the inner sphere and +Q on the outer spherical shell. a) Derive expressions for the electric field everywhere in space due to this charge configuration, indicating both direction and magnitude, in terms of the distance r from the center. Graph the electric field magnitude as a function of r. b) What is the surface charge density on the outer surface of the inner sphere and on the inner surface of the outer sphere? c) In part d) you will calculate the potential difference AV between the inner and outer conductors. Before you calculate the value, indicate what the sign (positive or negative) of AV=Vb – Va must be and give a clear explanation as to why.
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Transcribed Image Text:2. A spherical capacitor consists of an inner solid conducting sphere of radius a surrounded
by a spherical conducting shell of inner radius b and outer
radius c. The capacitor is charged with -Q on the inner sphere
and +Q on the outer spherical shell.
a) Derive expressions for the electric field everywhere in space
due to this charge configuration, indicating both direction and
magnitude, in terms of the distance r from the center. Graph
the electric field magnitude as a function of r.
b) What is the surface charge density on the outer surface of the
inner sphere and on the inner surface of the outer sphere?
c) In part d) you will calculate the potential difference AV between the inner and outer
conductors. Before you calculate the value, indicate what the sign (positive or negative)
of AV=Vb – Va must be and give a clear explanation as to why.
d) Determine the potential difference AV=Vb – Va between the inner and outer conductors.
e) From the result in d), determine the capacitance of this device and the energy stored in it.
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