Question

A solid insulating sphere of radius a carries a net positive charge +2Q, uniformity distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b and outer radius c, having a net charge of -3Q. Let the variable r represent the radial variable defined from the center of the sphere to an arbitrary point of interest defined by the following questions.

A) Derive an expression for the electric field only in terms of the given quantities and fundamental constants in the following regions:

i) r > c ( i.e outside of the shell)

ii) b < r < c ( i.e within the material of the shell)

iii) a < r < b ( i.e outside the sphere, inside the shell)

iv) r < a (I.E WITHIN THE MATERIAL of the sphere)

Box, label each electric field expression with the corresponding region.Explain your reasoning.

B) Derive an expression for the inner ( phi inner) and outer ( phi outer) surface charge density of the conducting shell only in terms of the given quantities and fundamental constants. Box all final expressions and explain your reasoning.

C) If a positive test charge, +q0, was placed in the region a < r< b, derive an expression for the electric force exerted on the test charge in terms of the given quantities and fundamental constants. Specify the direction in your expression with a unit vector. Based on your result, does the conducting shell have any influence of the force exerted on +q0? Explain your reasoning.

Answer 1

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