two point charges q1 = -5q and q2 = +2q are separated by distance d.?

Question

Separation of d

Two point charges q1 = -5q and q2 = +2q are separated by distance d. Locate the point (measured from the origin at q1) at which the electric field due to the two charges is zero.
x = _________d


Section 23.5 The Electric Field Due to Multiple Charges

Answer 1

You find the electric field from each charge and vector sum them. In this case there will be many points at which the fields cancel out if we consider points away from the q1 - q2 axis. I will get the result for the on-axis zero point only.

The field due to q1, E1 = -5q/(4*pi*e0*x^2)

The fileld due to q2, E2 = 2q/(4*pi*e0*(x-d)^2

It helps here to look at the geometry of the situation. The field from q1 will be in the direction toward q1, while the field from q2 will be in the direction away from q2. Therefore the fields cannot cancel anywhere between the two charges, where "away from q1" is the same direction as "toward q2". The fields can cancel at some point on axis on either side of q1 or q2,

For cancellation E1 must equal -E2

-5q/(4*pi*e0*x^2) = -2q/(4*pi*e0*(x-d)^2

simplify

5/x^2 = 2/(x-d)^2

or

5(x-d)^2 = 2x^2

5x^2 -10xd + 5d^2 = 2x^2

3x^2 - 10xd + 5d^2 =0

The solution is x = d*[10 +/- sqrt(40)]/6

This gives two answers: x = 2.721d and x = .613d

Based on the geometric reasoning above, x cannot be less than d, so the answer is x = 2.721d

Answer 2

2 element prices lie alongside the y axis. A fee of q a million = -13.ZeroµC is at y = 7.0 m,and a cost of q 2 = -4.0 µC is at y = -4.0 m. come around the point (really than infinity) at whichthe finished electric powered self-discipline is 0. Y =