# E-Fields Question

## Homework Statement

Two charges, charge one is +Q and charge two +2Q, are fixed in a plane along the y axis of an x-y coordinate plane. Charge one is at point (0,a) and Charge two is at the point (0,2a).
(a) Is there any portion of the y-axis in which the total electric field is zero? If so, where?
(b) If a small negative charge, -q, of mass m were placed at the origin, determine its initial acceleration (magnitude and direction).

## Homework Equations

E1=E2
F=ma
E=F/q
E=1/4pi(epsilon not)xQ/r^2

## The Attempt at a Solution

For (a), there will always be an e-field along the y-axis except for a point in between the two charges. I am having trouble finding that point, though. I set the two e-fields equal to each other, but was unsure of what to put as the radius for each.

For (b) I used F=ma and then plugged in F=Eq to get a=Eq/m. My final answer was (-1/4pi(epsilon not)x(Q/a^2+Q/2a^2)xq)/m.

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Matterwave
Gold Member
For a) You can use symmetry conditions to find that point. Just think about it logically, where should the E-field go to zero if the 2 charges are equal?

b) Your method is correct. I don't get why you would have an A there since both charges are +Q? Also, the 2a^2 in the denominator of the second term should have parenthesis: (2a)^2

For (b) the capital A was supposed to be a Q. And I also mistyped the question--the second charge is +2Q.

Matterwave
Gold Member
Ok, then for a)

You have for one charge: E1=kQ/r1^2 and E2=2kQ/r2^2 right. Since you are contained on the y-axis, the distance from a point on the y-axis to your charge 1 and 2 is r1 and r2. That should be relatively easy to find. The variable is y. Find a y such that the two are equal.

I think I am still confused on what to substitute for r1 and r2. Should one be y and the other (a-y)?

Matterwave