easy physics question about electric fields?

Question

A charge of −4.13 μC is located at the
origin, and a charge of −7.06 μC is located
along the y axis at 1.90962 m.
At what point along the y-axis is the electric
field zero?
Answer in units of m.

Answer 1

Since the charges have the same sign, and the field from each source varies as the inverse square of the distance from that source, we solve this problem as follows.

Call the charge at the origin Q0 and the other one Q1.

Let the FRACTIONAL distance from the origin to the other charge be f, then

Q0 / f^2 = Q1 / (1 - f)^2, leading to a quadratic equation:

1 - 2f + f^2 = Q1/Q0 f^2.

It is now convenient to define z = 1 / f. The quadratic equation then becomes

z^2 - 2 z + (1 - Q1 / Q0) = 0.

The roots of this are z = [2 +/- sqrt (4 - 4 (1 - Q1 / Q0))] / 2 or:

z = 1 +/- sqrt (Q1 / Q0) (!)

Since Q1 > Q0, only the ' + ' sign is relevant. (Actually, the neutral point being BETWEEN the charges, we know that f < 1, so that we need z > 1, whether or not Q1 > Q0.)

So z (= 1 / f) = 1 + sqrt (7.06 / 4.13) , so f = 1 / [1 + sqrt (7.06 / 4.13)]

= 0.4333776... .

Therefore the neutral point is at y = 0.4333776... x 1.90962 m

= 0.828... m. QED

(Note that since the charges are only given to 3 sig. figs., the physical answer is really accurate only to that number of figures. However, the mathematical result was 0.827586... m.)

Live long and prosper.

Answer 2

♦ you are a good boy ferret, start doing your homework yourself, I’m your teacher; du bist ein faul dumpkopf, wird fleißig aber!

Answer 3

i agree