Net Electric Field at 4 cm from a 40 nC Charged Particle A - Homework Solution

[-EquinoX-]

Homework Statement

if I have two charged particles A and B and are distanced 8 cm apart. At a point 4 cm from
A, the net electric field is 0. The charge of A is 40 nC. What can we conclude about the charge of B?

Homework Equations

The Attempt at a Solution

From my point of view B can be 40nC as well.. however I am not sure if there are some other answers as well. I am pretty sure there can be more than 1 answer

 

[Dick]

There are two points that are 4cm from A where the fields can cancel. They can cancel at the midpoint of A and B or they can cancel 4cm away from A on the opposite side of A from B.

 

[-EquinoX-]

hmm..not clear on what you meant here.. do you mind giving me a picture? how about B's charged magnitude? how large does it have to be?

 

[Dick]

I'm not very good at pictures. Suppose the charges are on the x-axis. Put A at x=0cm and B at x=8cm. Then the third location could be either at x=4cm or x=(-4)cm. If x=4cm, I agree with you, the charges should be equal. How about at x=(-4)cm?

 

[-EquinoX-]

well if it's at -4cm then the distance between A and B is only 4 cm away right? A is at 0 and B is at -4?

 

[Dick]

No, A stays at 0cm and B stays at 8cm. Call the third point C=(-4)cm. C is 4cm from A and 12cm from B, right? What does the charge at B have to be to cancel the E field at C?

 

[-EquinoX-]

I get the picture you're trying to say now. However...how do I calculate the magnitude of B based on that info??

 

[Dick]

Use E=k*Q/r^2. You know the distance r for each charge and you know Q for A is 40nC. Write an equation that they sum to zero and solve for the charge at B.

 

[-EquinoX-]

so EA + EB = 0
k*40/4^2 + k*X/12^2 = 0

and I need to solve for X?

 

[Dick]

Yeah, sure. Solve for x!

 

[-EquinoX-]

okay the answer I got is 360nC, is that right? and are those the only two points from A where the fields cancels?

 

[Dick]

I get -360nC, don't you? The sign is important. At any other point besides those two there is an angle between the two E fields. Can two fields cancel if they are are at different angles?

 

[-EquinoX-]

yes, I missed the negative signs.. as far as I know they can't cancel if it's at a different angles.. correct?

 

[Dick]

Yes. Two vectors can only cancel if they are negatives of each other. So they have to point along the same line.

 

[-EquinoX-]

okay.. so the conclusion is only these two, where B is 40nC and B is -360nC

 

[Dick]

Seems so to me. Ok with you?

 

[-EquinoX-]

Seems fine with me, I am just worried that I missed some answers.