The figure shown is a section of a conducting rod of radius R_1 = 1.30 mm and le
ID: 1530227 • Letter: T
Question
The figure shown is a section of a conducting rod of radius R_1 = 1.30 mm and length L = 11.00 m inside a thick-walled coaxial conducting cylindrical shell of radius R_2 = 10.0 R_1 and the (same) length L. The net charge on the rod is Q_1 = + 1.90 times 10^-12 C; that on the shell is Q_2 = -4.00 Q_1 What is the magnitude E of the electric field at a radial distance of r = 2.50 R_2? What is the direction of the electric field at that radial distance (inward, outward, or zero)? Give reasons! What is the magnitude E of the electric field at a radial distance of r = 3.50 R_1? What is the direction of the electric field at that radial distance (inward, outward, or zero)? Give reasons!Explanation / Answer
(a)
at r = 2.5*R2,
curved surface area of cylinder is,
A = 2*pi*r*L = 2*pi*2.5*R2*L
A = 50*pi*R1*L = 50*3.14*1.3*10^(-3)*11
A = 2.245 m^2
Qenc = Q1 - 4Q1 = -3Q1
Qenc = -3*1.9*10^(-12) = -5.7*10^(-12) C
according to gauss's law,
phi = E.A = Qenc / e0
E = Qenc / A*e0
E = -5.7*10^(-12) / 2.245*8.85*10^(-12)
E = -0.286 N/C
(b)
negetive sign of E indicate that direction is inward.
(c)
at r = 3.5R1
A = 2*pi*(3.5*R1)*L
A = 0.314 m^2
E = 5.7*10^(-12) / 0.314*8.85*10^(-12)
E = 2.05 N/C
(d)
positive sign of E indicate that direction is outward.