A thin cylindrical shell of radius R_1 = 65 cm is surrounded by a second cylindr

Question

A thin cylindrical shell of radius R_1 = 65 cm is surrounded by a second cylindrical shell of radius R_2 = 9.0 cm, as shown. Both cylinders are 5.0 m long; the inner one carries a total charge Q _1 = + 0.88 nC and the outer one Q_2= - 1.56 nC. For points, far from the ends of the cylinders, determine the electric field at a radial distance R from the central axis of (a) 3.0 cm, (b) 7.0 cm, and (c) 12.0 cm. Be sure to indicate the direction (inward or outward) as well as the magnitude of the electric field.

Explanation / Answer

using gauss law

Electric flus is Phi_E = E*A*cos(theta) = Q_inside/eo

theta is the angle between the surface area and Field ,in this problem theta = 0

E*A = Q_inside/eo

eo is the permittivity of free space

A = surface area of the cylinder = 2*pi*R*L

then

a) at 3 cm

E*2*pi*R*L = q_Inside/eo

(E*2*3.142*0.03*5) = (0.88*10^-9)/(8.85*10^-12)

E = 105.5 N/C outward

b) at 7 cm

E*2*pi*R*L = q_Inside/eo

(E*2*3.142*0.07*5) = ((0.88-1.56)*10^-9)/(8.85*10^-12)

E = -34.93 N/C
E = 34.93 N/C inward
C) x = 12 cm

E*2*pi*R*L = q_Inside/eo

(E*2*3.142*0.12*5) = ((0.88-1.56)*10^-9)/(8.85*10^-12)

E = 20.4 N/C inward

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