The point where the electric field between two charged spheres is zero

[bandit101]

Homework Statement

Sphere A, with a positive charge is located close to another Sphere B, with positive charge. The relative size of the charges is such that the charge on Sphere A = 4 (Sphere B). Locate Point P between the two spheres where the force exerted by the field is zero. State the location of Point P in terms of the center of A and B.

Homework Equations

These are the equations I have to work with:

F = k (Qq)/d2

where:

* K = 9 x 10^9 Nm^2/C^2(constant),
* Q = electric force of one object (C),
* q = electric force of the other object (C),
* d = distance between the two objects (m).

E = F/q

The Attempt at a Solution

I had no clue of how to go about this without an actual given distance. I tried finding the E of each charge with d^2 still in it then add those two to equal zero, but it didn't work. All of the example I have found have either had a positive and negative charge or a given distance. How would I solve this?

 

[diazona]

I had no clue of how to go about this without an actual given distance. I tried finding the E of each charge with d^2 still in it then add those two to equal zero, but it didn't work.

When you add the electric fields (that's what you mean by E, right?), remember that they are vectors, not just numbers. So when you add them, it's not as simple as just adding the magnitudes; you need to take into account the relative direction of the two fields.

Try drawing a picture of the two spheres and the point P, and include the direction of the electric field at point P due to each sphere separately.

 

[bandit101]

So would the direction be part of d? Wouldn't the d^2 just cancel out because they are common denominators?

 

[bandit101]

I don't think I understand. Even if I try to add them as vectors, whenever there is a zero in the equation it doesn't work because zero divided by anything is zero.

 

[bandit101]

Okay so there is a picture that goes along with this question. I didn't know if it was that important because I wasn't given a distance. But I measured it with my ruler. From the center of the two spheres, they are 5.8cm apart and from the edges of each, they are 4cm apart. I would use the 5.8cm measurement right?


So, would I then go:


E_A=kQ₁/d²
E_A=4k/d²

E=kQ₂/d²
E=k/(d+5.8)²

Then would I go:

E_A - E_B = 0
4k/d² - k/(d +5.8)² = 0
4k/d² = k/(d +5.8)²
4/d² =1/(d² + 11.6 + 33.64)
[(d² + 15.24)(4)]/d² = 1
(4d² + 60.96)/d² = 1
4d² + 60.96 = d²
3d² + 60.96 = 0
(3)(d² + 20.32) = 0

So:
d² + 20.32 = 0
d² = -20.32
d = 4.507771...

Is this right?

So if Sphere A was at 0cm and Sphere B was at 5.8cm, then Point P would be at 4.5cm?