Can Electric Forces Cancel with Opposite and Like Charges?

[wazzup]

Q1) Consider two points charges of the same magnitude but oppsite sign ( +Q and -Q), which are fixed a distance d apart.

A) Can you find a location where a third positive charge Q could be placed so that the net electric force on this third charge is zero?
B) What if the first two charges are both +Q?

The answers for A is : No
The answer for B is : yes, midway between them.

I don't understand how they got this anwer. Is A, no because the oppsite charges cancel each other out?

For B, since all three charges will be positive, how can the net electric charge be 0?I'm confused...

__________________________________________________________________________________________________________Q2) In a capacitor, why is there a distance betwene the two plates? I suppose this is so that an equal and opposite charge can exist? how does having two plates sepreated by a distance create an equal and opp charge in the two plates?

What if there was no distance between them? Then will they have same type of charge?

Thanks much.

 

[finchie_88]

You got the right answer of A. From a slightly more mathematical perspective:
$$\frac{kQ}{r^2} = \frac{-kQ}{(d-r)^2}$$ Where d is the total distance between both of the charges, and r is distance between the "test charge" and one of the charges.
$$\therefore \frac{1}{r^2} = \frac{-1}{(d-r)^2}$$
$$2r^2 - 2rd +d^2 = 0$$
$$r = \frac{2d \pm \sqrt{-4d^2}}{4}$$
Obviously, the negative square root means that it is imaginary, and so there exists no such position.

For B, repeat the same procedure as before, except that the second charge will be +Q, you are right, you should get the answer d/2. The reason is that the electric field stength from both are positive (hence repulsive to a test charge), and that at d/2, they are exactly equal in size, but opposite in direction.

In a capacitor, the gap creates a uniform electric field, and it is within this field that energy can be stored, and so if you disconnect the power supply, charge can still flow for a short time (if there was no resistance in the circuit, the current would keep on going, that is what superconductors are - materials with zero resistance). If they were not separated by an insulator, and the electric field between them would not be generated.

 

[wazzup]

I see. thanks much..