Physics problem: Electric Forces and Electric Fields?

Question

hi. i really need help with a couple of problems. i can't seem to figure these out at all.

okay, here's the first one:

Two charges, -14 and +4.4 µC, are fixed in place on the x axis at x = 3.0 m and x = 0 m, respectively.

(a) At what spot along the x axis is the net electric field zero?

(b) What would be the force on a charge of +15 µC placed at this spot?


the other question is:

A tiny ball (mass = 0.014 kg) carries a charge of -22 µC. What electric field (magnitude and direction) is needed to cause the ball to float above the ground?





If you could help me with either of those problems or both, it would be really helpful. thanks.

Answer 1

So charge 4.4 µC is at x = 0 and charge -14 µC is at x = 3.0.
(a) Electric field along the x-axis is:
E(x) = 10^(-6)/(4*pi*eo)(4.4/x^2 - 14/(x-3)^2)
set it to zero, we have: 4.4(x-3)^2-14x^2 = 0
9.6x^2+26.4x-39.6 = 0
The solutions to this quadratic equation are:
x1 = 1.08 (m) and x2 = -3.83 (m)
So the net electric field is zero at both x1 and x2.

(b) Zero.

The other question: In this case the upward electric force must be the same as the gravitational force:
0.014*9.8 = 2.2x10^(-6)*E
Solve for E, which must be directed downwards.