3. a) Sketch the electric field in the interior and the exterior of a hollow sph

Question

3. a) Sketch the electric field in the interior and the exterior of a hollow spherical metal shell 6 cm in radius if the shell has a net charge of +10* Coulombs on its surface. a) What is the electric field at r-o? b) Find the surface charge density on the shell. c) What is the electric field strength at the surface R = 6 cm? d) What is the voltage at the surface of the sphere? Assume the potential goes to zero at infinity. e) What is the voltage at the origin, r-02 How does it compare to the voltage at the surface R-6 cm? Justify your answer. f) Sketch the voltage as a function of position from r-0 to r-R, then for values ofr-R out to r = 10 R. How does the value of voltage at 10 R compare to the value of R? Justify your answer.

Explanation / Answer

a) at r = 0, E = 0

b) surface charge density on the shell,

sigma = Q/Area

= Q/(4*pi*R^2)

= 10^-8/(4*pi*0.06^2)

= 2.21*10^-7 C/m^2

c) E = k*Q/R^2

= 9*10^9*10^-8/0.06^2

= 2.50*10^4 N/c

d) V = k*Q/R

= 9*10^9*10^-8/0.06

= 1.50*10^3 V

e) at r = 0, V = 1500 V

at R = 6 cm, V = 1500 V

inside elctric field is zero. so, elctric potential is constant at every point inside the shell.

f) at r = R, V = k*Q/R = 1500 V

at r = 10*R, V = k*Q/(10*R) = 150 V

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