The figure below is a section of a conducting rod of radius R 1 = 1.30 mm and le

Question

The figure below is a section of a conducting rod of radius R1 = 1.30 mm and length L = 11.00 m inside a thick-walled coaxial conducting cylindrical shell of radius R2 = 10.0R1 and the (same) length L. The net charge on the rod is Q1 = +1.70 1012 C; that on the shell is Q2 = 3.00Q1.

(a) What is the magnitude E of the electric field at a radial distance of r = 1.50R2?
1 N/C

(b) What is the direction of the electric field at that radial distance?
2---Select---inwardoutward

(c) What is the magnitude E of the electric field at a radial distance of r = 4.50R1?
3 N/C

(d) What is the direction of the electric field at that radial distance?
4---Select---inwardoutward

(e) What is the charge on the interior surface of the shell?
5 C

(f) What is the charge on the exterior surface of the shell?
6 C

Explanation / Answer

linear charge density of inner rod, lamda1 = Q1/L

= 1.7*10^-12/11

= 1.545*10^-13 c/m

linear charge density of outer shell, lamda2 = -3*Q1/L

= -3*1.7*10^-12/11

= -4.64*10^-13 c/m

a) at r = 1.5*R2

E = 2*k*(lamda1+lamda2)/r

= 2*9*10^9*(1.545*10^-13 - 4.64*10^-13)/(1.5*10*1.3*10^-3)

= 0.2857 N/c

b) inward

c) at r = 4.5*R1

E = 2*k*lamda1/r

= 2*9*10^9*(1.545*10^-13)/(4.5*1.3*10^-3)

= 0.4754 N/c

d) outward

e) charge on inner surface of the shell = -Q1

= -1.7*10^-12 C

f) charge on outer surface of the shell = -2*Q1

= -2*1.7*10^-12 C

= -3.4*10^-12 C

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