A point charge q 1 = -5.7 C is located at the center of a thick conducting shell

Question

A point charge q1 = -5.7 C is located at the center of a thick conducting shell of inner radius a = 2.9 cm and outer radius b = 4 cm, The conducting shell has a net charge of q2 = 2.8 C.

1) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 6.3 cm along the x-axis from q1?

2) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 6.3 cm along the x-axis from q1?

3) What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.45 cm along the y-axis from q1?

5) What is b, the surface charge density at the outer edge of the shell?

Explanation / Answer

(1)

Ex(p) = k*q2/x^2 = 9*10^9*2.8*10^-6/0.063^2 = 6349206.35 N/C

(2)

Ey(p) = 0

(3)

Ey(R) = -k*q1/y^2 = -9*10^9*5.7*10^-6/0.0145^2 = -243995243.8 N/C

(5)

Qinner = +q1

Qinner + Qouter = q2

Qouter = q2 - Qinner = 2.8 - 5.7 = -2.9 uC

sigma_b = Qouter/(4*pi*b^2)

sigma_b = -2.9*10^-6/(4*pi*0.04^2) = -0.000144 C/m^2

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