A point charge q 1 = -5.6 C is located at the center of a thick conducting shell

Question

A point charge q1 = -5.6 C is located at the center of a thick conducting shell of inner radius a = 2 cm and outer radius b = 4.1 cm, The conducting shell has a net charge of q2 = 2.9 C.

1)

What is Ex(P), the value of the x-component of the electric field at point P, located a distance 6.6 cm along the x-axis from q1?

N/C

2)

What is Ey(P), the value of the y-component of the electric field at point P, located a distance 6.6 cm along the x-axis from q1?

N/C

3)

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

N/C

4)

What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1 cm along the y-axis from q1?

N/C

5)

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

C/m2

6)

What is a, the surface charge density at the inner edge of the shell?

C/m2

Explanation / Answer

We know that the field of a point charge is given by:

E = kq/r^2

1)Ep = k (q1+q2)/r^2

Ep-x = 9 x 10^9 x 10^-6 (-5.6 + 2.9)/0.066^2 = -5.58 x 10^6 N/C

Hence, Ep-x = - 5.58 x 10^6 N/C

2)Ep-y = 0

3)Ex(R) = 0

4)Ey(R) =

[Epy = Ex(R) = Ey(R) = , since the field inside any conductor is zero]

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