A solid conducting cylinder of length 10.0 cm and of radius 5.0 cm has a net cha

Question

A solid conducting cylinder of length 10.0 cm and of radius 5.0 cm has a net charge of 2.0 mu C uniformly distributed throughout the cylinder This cylinder is surrounded by a much larger conducting cylinder (inner radius of 12 cm and outer radius of 16 cm) that has a net charge of 4.0 mu C. If the system reaches equilibrium, find A) The charge on the inside and outside surface of the conducting sphere, and B) the electric field at points A, B, C, D with the following radii: r_A+ = 4.0 cm, r_B = 7.5 cm, r_c = 14 cm, and r_D = 20 cm.

Explanation / Answer

(A)

Qinner = -Qsolid = -4 uC

Qouter + Qinner = 2 uC

Qouter- 4uc = 2 uC

Qouter = 6 uC

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(B)

for solid cylinder

ar r inside the cylinder

Qinside = Q*r^2/R^2

using gauss law

Einside*2*pi*r*L = Qinside/eo

Einside = 2*k*Q*r/(L*R^2)

out side the solid cylinder

Qinside = Q

using gauss law

Einside*2*pi*r*L = Qinside/eo

Einside = 2*k*Q/(r*L)

(B)

ra = 4cm < 5 cm

Einside = 2*9*10^9*2*10^-8*0.04/(0.05^2*0.1)= 57600 N/C

rb = 7.5 cm > 5

Eoutside= 2*9*10^9*2*10^-6/(0.075*0.1) = 4800000 N/C

rc = 14 cm inside the conducitng cylinder

Inside the conductor the electric field = 0

Ec = 0

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rd = 10 cm > 16 cm

Ed = k*Qnet/rd^2

Ed = 9*10^9*2*10^-6/0.2^2 = 450000 N/C

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