Physics....electric fields question...aaaah?

Question

two point charges,-16 and +4.0 microC, are fixed in place and separated by 3.0m.

A. at what spot along a line through the charges is the net electric field zero? Locate this spot relative to the positive charge. The spot does not necessarily lie between the two charges.

b. What would be the force on a charge of +14microC placed at this spot?`

Answer 1

A.

Though the spot does not necessarily lie between the two charges, it has to lie on the line passing through the two charges.

As the direction of the field due to the positive charge is away from it and towards the negative charge and as the negative charge is larger in magnitude, the point has to be on the other side of the negative charge on the line joining the two charges.

Let x = its distance from the positive charge

=> 3 + x = its distance from the negative charge

=> k*4/x^2 = k*16/(3 + x)^2

=> (x + 3)^2 = 4x^2

=> 3x^2 - 6x - 9 = 0

=> x^2 - 2x - 3 = 0

=> (x - 3)(x + 1) = 0

=> x = 3 m (as x cannot be negative)

B.

Force on any charge at that spot will be zero as the field is zero.