Electric field calculation for 3 point charges

[vf_one]

Hi I'm having difficulty understanding why the solution for the answer to the following problem is worked out this way.

Three spheres are placed at fixed points along the x axis, whose positive direction points towards the right.

Sphere A is at x=47cm with a charge of 5x10^-6C
Sphere B is at x=50cm wtih a charge of -5x10^-6C
Sphere C is at x=54cm with a charge of 10x10^-6C

Sphere B is removed. What would be the magnitude of the electric field at the point where sphere B was located?

I've managed to work out the electrostatic force on sphere B using F= kq_Aq_B/r² and F= kq_Bq_C/r².

In the answer it says that we use the equation E=F_B/q_B. I don't understand why we use the electrostatic force on sphere B and the charge of sphere B to work out the electric field since B is removed and only spheres A and C are left.

Can anyone explain this to me?
Thanks

 

[kuruman]

In the answer it says that we use the equation E=F_B/q_B. I don't understand why we use the electrostatic force on sphere B and the charge of sphere B to work out the electric field since B is removed and only spheres A and C are left.

Can anyone explain this to me?
Thanks

To figure out if there is an electric field at a point in space, in what direction it points and how strong it is, you need to bring a positive test charge of known value q at that point and measure the force on that charge. The magnitude of the force divided by the value of the test charge is (by definition) the magnitude of the electric field. The direction of the force is the direction of the electric field. So this question describes exactly this process with sphere B being the test charge.

 

[vf_one]

We didn't go over this in class so this really helped. Thank you!