Net Force on a Charge at a Given Point from Two Other Charges

[steve92595]

This was on a test i took yesterday, and my friends and I could not figure it out. What we want to know is if it is possible to figure out the net force on a charge (q3) at (X+3.3,0) from two charges (q1, q2), if you are given: the value for q3, the electric field caused by q2 on point x, and the electric field caused by q1 on point x.

i spent about 30 miniutes trying to figure this out, but without any value for r or q1/q2 i saw no way to accomplish this question without making up values.

 

[jamesrc]

Telling you what the electric charge due to q1 is at x is the same as telling you how far q1 is from x:

Remember:

$$|\vec E(r)| = k\frac{q_s}{r^2}$$

where qs is the source charge. That should help you solve the rest of the problem.

 

[steve92595]

But I wasn't given r nor was i given qs, unless qs is supposed to be q3 (the only charge value i was given), but that doesn't seem right to me because q3 doesn't affect the electric field value

 

[jamesrc]

Ok, I didn't read it all the way; I thought you had q1 and q2.

Let me ask you this: are q1 and q2 in the same spot? That seems implied by your problem statement, but I'm not sure. Like, are q1 and q2 at the origin (0,0) and q3 is at (x+3.3, 0)?

 

[steve92595]

ok, sorry left out a lil information. they are not at the same spot. what the question gave was that the electric field from q1 created a force on X at 12 degrees and the electric field from q2 created a force on X at -36 degrees. if I'm not being very clear, well the question wasn't clear at all, so just ask.

 

[NateTG]

Originally posted by steve92595
This was on a test i took yesterday, and my friends and I could not figure it out. What we want to know is if it is possible to figure out the net force on a charge (q3) at (X+3.3,0) from two charges (q1, q2), if you are given: the value for q3, the electric field caused by q2 on point x, and the electric field caused by q1 on point x.

i spent about 30 miniutes trying to figure this out, but without any value for r or q1/q2 i saw no way to accomplish this question without making up values.

If you have a little bit of extra information - like that the charges are all in a line -, then the problem is solvable.

The notation you used in the post is confusing - you use X and x, and it's unclear whether they're interchangable. In addition youhave (X+3.3,0) which might be a vector sum, or a displacement in the x dimension, or something different entirely. Then (q1,q2) is confusing because it looks like a vector, but is probably a list of charges to deal with.

Do you know the magnitude of the forces?

 

[steve92595]

Sorry, I didn't even realized i had capitalized some X's and not others. They are all referring to a point, not specified where, so i just set it to (X,0). And although that was realatively confussing the way i described it, it was 10 times better than the way it was on the test.

No i was not given the magnitude of q1 nor q2. All i know is that q1 creates an electric field of 2.0*10^-5 N/C on point (X,0) at 12 degrees. q2 creates an electric field of 3.0*10^-5 N/C on point (X,0) at -36 degrees. I was trying to find what the net force would be on a charge (q3) of 4.7*10^-9 C at (X+3.3,0). This was all that was given to me on the test. The positions of q1 and q2 were not given, however it can be assumed that q1 is at some point -168 degrees from point (X,0) at distance r1 from (X,0). Also q2 would be at a point 144 degrees from point (X,0) at distance r2 from (X,0)

hope this is easier to understand

 

[NateTG]

Why are you introducing X, just make the point (0,0).

That said, it really sounds like you somhow misread the problem.