Calculating Electric Field Zero Point for Negative Point Charges

[Dayton]

Homework Statement

A one point charge of -12µC is located at x=0m and a second point charge of -24µC is located at x=6m. Calculate the point where the electric field would be zero.

I think that my physics professor worded this question wrong. Is there a point where the field would be zero if both of the charges are negative?

Homework Equations

The Attempt at a Solution

 

[x_engineer]

Yes, you would. That would be the point where the fields of the two charges exactly cancel, and would lie along the line between them. Remember the electric field is a vector, and you have to take into account the direction when you combine them. Along the line between them, the directions are exactly opposite, so that would be where

q1/(r1**2)=q2/(r2**2)

You might be thinking of the potential with respect to infinity. Potential is a scalar, and the potential of two like charges cannot cancel.

 

[NascentOxygen]

If you can place a positive charge somewhere, and find it does not want to move from that spot (because it is not attracted and is not repelled), then that location would have zero electric field. Suppose you tested a spot midway between two equal point charges, your test charge would be equally attracted to each, so with no nett force acting on it, it would not move. So the field there would be zero. And you could find lots of other locations where the test charge experienced no nett force, too.

 

[Dayton]

Okay, so I set up the following equation:

r1=6m-r2

Q1/(6m-r2)^2 = Q2/(R2^2)

Q1 (R2)^2 = Q2 (6m-R2)^2

0 = 36*Q2 -Q2*2R2+Q2*(R2)^2 -Q1*(R2)^2

Every time I try to solve using the quadratic, I end up getting a negative number under the radical. What am I doing wrong? Any help would be greatly appreciated.

 

[Dayton]

I got the answer, guys. Thanks for leading me in the right direction.

 

[Gagandeep sin]

the electric field at a given point is found to be a zero. is it true to say that there are no charges in other point. please justify answer with suitable answer. please urgent

 

[NascentOxygen]

the electric field at a given point is found to be a zero. is it true to say that there are no charges in other point. please justify answer with suitable answer. please urgent

Are there some words missing, here?

 

[JHamm]

the electric field at a given point is found to be a zero. is it true to say that there are no charges in other point. please justify answer with suitable answer. please urgent

If you mean that having a point where the electric field is zero implies that there are no charges in the system then no, this thread has demonstrated that two charges can create a point with zero electric field.