An infinitely long, solid cylinder of charge with constant positive charge density, po, is concentric with an infinite cylindrical shell of charge per unit length, -A, where A is a positive quantity. Both cylinders have their axes aligned with the z axis. The radius of the solid cylinder is a and that of the shell is b. Assume b > a.

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Please write you answers neatly and answer all parts.

a) Find the electric field (vector) as a function of radial distance, r, from the z axis. You may
provide your answer in piecewise form, but account for all values of r.
b) Find the electric potential as a function of radial distance, r, from the z axis for r < b taking
P(r=0) = 0.
c) Under what condition on the parameters of the problem will the electric field outside the
cylindrical shell be zero?
d) For the situation in part c,what is the electric potential as a function of r, for r> b.
e) For the situation in part c, evaluate the potential energy per unit length (along the cylinders)
associated with the arrangement of charges.
Transcribed Image Text:a) Find the electric field (vector) as a function of radial distance, r, from the z axis. You may provide your answer in piecewise form, but account for all values of r. b) Find the electric potential as a function of radial distance, r, from the z axis for r < b taking P(r=0) = 0. c) Under what condition on the parameters of the problem will the electric field outside the cylindrical shell be zero? d) For the situation in part c,what is the electric potential as a function of r, for r> b. e) For the situation in part c, evaluate the potential energy per unit length (along the cylinders) associated with the arrangement of charges.
An infinitely long, solid cylinder of charge with constant positive charge density, po, is
concentric with an infinite cylindrical shell of charge per unit length, -A, where A is a
positive quantity. Both cylinders have their axes aligned with the z axis. The radius of
the solid cylinder is a and that of the shell is b. Assume b > a.
Po
Transcribed Image Text:An infinitely long, solid cylinder of charge with constant positive charge density, po, is concentric with an infinite cylindrical shell of charge per unit length, -A, where A is a positive quantity. Both cylinders have their axes aligned with the z axis. The radius of the solid cylinder is a and that of the shell is b. Assume b > a. Po
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