Expression of Electric Field with known charges

[Alexstre]

Homework Statement

I have 2 charges:
Q1 = 300 uC located at (1, -1, -3) m
Q2 = ?? uC located at (3, -3, -2) m

Q1 feels a force from Q2 of F1=(8i - 8j + 4k) N

1. Find Q2
2. Find the expression of the E-Field at (3, -3, -2) m (at Q2)

Homework Equations

F=(k|Q1*Q2|) / r^2
E=(k|q|) / r^2

The Attempt at a Solution

For the first part I've used the magnitudes:
Q1 = (1, -1, -3) m = $$\sqrt{1^2 + -1^2 + -3^2}$$
F1 = (8i - 8j + 4k = 4 N

I found the distance between Q1 and Q2 using pythagorean formula: 3 meters.
Then I solved for Q2 using Coulomb's Law:
Q2 = 13.3 uC

For the second part, I know that since they ask for the expression of the electric field at the location of Q2, Q2 will not contribute to the value. Beside that, I'm a bit lost.

Do I need to use the distance between Q1 and Q2, then solve for E=k|q| / r^2? What's |q| in this case?

Thanks!

 

[hikaru1221]

The E-field by both charges is not definite at the positions of the charges. I think if the question is given by your teacher, you should seek clarification from him whether he asks for the E-field by both or the E-field contributed by only Q1 (if the latter, ignore Q2 as you only count Q1 in the E-field by Q1). Otherwise, you should ignore the question, as it doesn't have an appropriate answer.

 

[Alexstre]

The E-field by both charges is not definite at the positions of the charges. I think if the question is given by your teacher, you should seek clarification from him whether he asks for the E-field by both or the E-field contributed by only Q1 (if the latter, ignore Q2 as you only count Q1 in the E-field by Q1). Otherwise, you should ignore the question, as it doesn't have an appropriate answer.

I'm assuming it's the latter; that I can ignore Q2 and only count Q1. I'm still not sure how to do it though. Is |q| in E=k|q| / r^2 simply the value of Q1?

Thanks!

 

[hikaru1221]

Do you have to count something else besides Q1 when calculating something created by only Q1?

EDIT: By the way, the question asks for the E-field which is a vector, not just its magnitude. You may find this formula helpful $$\vec{E}=k\frac{q}{r^3}\vec{r}$$

 

[rwisz]

Hello,

It seems like you are on the right track with your calculations. To find the expression for the electric field at the location of Q2, you can use the formula E=(k|q|) / r^2, where |q| is the magnitude of the charge at that location. In this case, since we are looking at the electric field at the location of Q2, |q| would be the magnitude of Q2, which you have already calculated to be 13.3 uC.

You can also use the distance between Q1 and Q2 to calculate the electric field at Q2. The distance between the two charges would be 3 meters, as you have correctly calculated. So the expression for the electric field at (3, -3, -2) m would be E=(k|Q2|) / (3)^2, where k is the Coulomb's constant.

I hope this helps. Keep up the good work!