Finding electric field and force at a point

[cherry_cat]

Homework Statement

A hollow ball with radius R = 2 cm has a charge of -2 nC spread uniformly over its surface (see the figure). The center of the ball is at P1 = <-3, 0, 0> cm. A point charge of 6 nC is located at P3 = <6, 0, 0> cm.
1.What is the net electric field at location P2 = <0, 4, 0> cm?
2.At a particular instant an electron is at location P2. What is the net electric force on the electron at that instant?
3. What is the direction of the net electric force on the electron? (Multiple choice)
a.The force is opposite to the direction of the net electric field at P2
b.The force is in the same direction as the electric field at P2
c.There is not enough information to determine the direction of the force
d.The force is at right angles to the direction of the electric field at P

Homework Equations

F=E/q
E=kq/r^2
F=k q1 q2/r^2

The Attempt at a Solution

For part 1: I am unsure how to find r for the sphere. I know you would add 2cm to the distance for a problem that has the distance from the outside of the sphere, but this question has vectors. Does this mean I can find r in the normal way, by subtracting the source location from the observation location.

For Part 3, as it is an electron, surely that means the force would be in the same direction and the answer would be b.

 

[ap123]

First of all, draw a diagram to make sure you know where everything is.
Work out the magnitude of the field produced by each charge at the point P2 and add as vectors.

The hollow ball can be replaced by a point charge at P1 (since the ball has spherical symmetry ).

For part 3, what is the (vector) equation relating electric force and electric field?