Question

A point charge q1 = -6.3 μC is located at the center of a thick conducting shell of inner radius a = 2.7 cm and outer radius b = 4.2 cm, The conducting shell has a net charge of q2 = 1.5 μC.

https://www.smartphysics.com/Content/smartPhysics/Media/Images/EM/04/h4_sphere_v3.png

1. What is Ex(P), the value of the x-component of the electric field at point P, located a distance 8.4 cm along the x-axis from q1?

2. What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.35 cm along the y-axis from q1?

Answer 1

Think Gauss's Law: \[\oint E \, dS = \frac{ q }{ \epsilon }\]
If you choose your surface cleverly, E will be constant and you can pull E out of the integral.