Need step by step solution with answers. 1. A charge Q is uniformly distributed

Question

Need step by step solution with answers.

1. A charge Q is uniformly distributed on the surface of a conducting spherical shell with outer radius R and inner radius R/2. Apply Gauss' law to justify your answers to the questions below.

a) What are the magnitude and direction of the electric field at a distance R/4 from the center of the sphere?

b) What are the magnitude and direction of the electric field at a distance 3R/4 from the center of the sphere?

c) What are the magnitude and direction of the electric field at a distance 2R from the center of the sphere?

2. A long, non-conducting of radius R=2.0cm carries a uniform charge density p=18uC/m^3. Assume that its length >>R. Calculate the electric field at distance r = 1.0 cm from the axis of the cylinder. Sketch the cylinder and the Gaussian surface used for your analysis.

Explanation / Answer

EF at KQr/R^3

for r = R/2 , EF = KQ/2R^2

a. at if r = R/4,

EF = KQ/2(R/4)^2 = 8 KQ/R^2

b. if R =3R/4

EF = KQ/2 (3R/4)^2 = 8KQ/9 R^2

c at r= 2R

EF = KQ/2R)^2 = KQ/4R^2

b.EF = rho r/ 2e0 = 18*10^-6/2*8.85*10^-12 = 1.016 *10^6 N/C

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