A conducting sphere of radius a has total charge - q and is located at the cente

Question

A conducting sphere of radius a has total charge - q and is located at the center of the spherical cavity of a hollow conducting sphere having inner radius b and outer radius c. The hollow sphere has total charge +Q. The system is in electrostatic equilibrium. The charge in the shell is larger than the magnitude of the charge on the sphere, Q > q. Give your answers in terms of the given quantities and k = 1/4 pi epsilon_0 Determine the magnitude of the electric field for the following regions, where r is the distance from the center, and state direction of fields. r

Explanation / Answer

1.) r<a

According to gauss law

Q' = Q *r^3/a^3

E.A = Q'(inclose)/epsilion

E = Qr / (4*pi*a^3*epsilon)

2.)a<r<b

E.A = Q(inclose)/epsilion

E = -q / 4*pi*r^2*epsilon

3.)b<r<c

E.A = Q(inclose)/epsilion

Q' = Q *{ (4*pi*r^3 /3 - 4*pi*b^3)} / { (4*pi*c^3 /3 - 4*pi*b^3)}

E.A = Q'(inclose)/epsilion

E = Q *{ (4*pi*r^3 /3 - 4*pi*b^3)} / { (4*pi*c^3 /3 - 4*pi*b^3)} / (4*pi*r^3*epsilon)

4.) r>c

E.A = Q(inclose)/epsilion

E = Q/ 4*pi*r^2* epsilion

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