Where Are the Zero Potential Points Located in a Two-Charge System?

[linemanpete]

ok I've "hit the wall" on this question and I am wondering if someone could help me

a +charge q1 is located 3.00m left of a -charge q2. the charges are not equal in magnitude. There is 2 spots on a line through the charges where the potential is 0. 1 spot on this line where the electric field is 0 is 1m to the right of q2. What are the 2 spots of 0 potential relative to the negative charge?

I realize that q1>q2 (magnitude) since the Electric field components cancel each other out to the right of q2
but from there I am very stuck

thanks

 

[StatusX]

Zero potential is not the same as zero field. Just find the total potential by adding the potential from each charge, plug in the first zero to get an equation relating q1 and q2, plug in for q2, and then solve for the second zero. You shouldn't need to know q1 to get the second zero, since you should be able to factor it out front. Also, don't forget the potential depends on the absolute value of the difference in position, or you'll only be able to find one zero.

 

[wais]

for any help

The two spots on the line where the potential is 0 relative to the negative charge are 1m to the left and 1m to the right of q1. This is because the electric field from q1 and q2 at these points will cancel each other out, resulting in a net electric field of 0.

To find the potential at a certain point on the line, you can use the formula V = kq/r, where V is the potential, k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the point to the charge.

In this case, we can set up two equations:
V1 = kq1/r1 = kq2/(3.00 + r1)
V2 = kq1/r2 = kq2/(3.00 - r2)

Since we know that V1 = V2 = 0, we can solve for r1 and r2:
r1 = 3.00q2/(q1 - q2)
r2 = 3.00q2/(q1 + q2)

Substituting in the values of q1 and q2, we get:
r1 = 3.00(1.00q2)/(2.00q2) = 1.50m
r2 = 3.00(1.00q2)/(4.00q2) = 0.75m

Therefore, the two spots of 0 potential relative to the negative charge are 1.50m to the left and 0.75m to the right of q1.