hi -- thank you for your help before-- that makes sense--

also, im stuck on this: if there is a negative2.5 microcoulomb charge 1 m away from a 6microcoulomb charge, then at what point (other than infinity) is the electric field = zero?
Sorry, i have no idea how to do this, i tried finding F using Kq1q2/ r^2 but im not sure what is next...or if that is even correct..?

WEll, E is a vector. If the charges are the same, between them the individual E are in opposite directions, so if at the right point, E adds to zero

k*2.5E-6/x^2 -k6E-6/(1-x)^2=0
solve for x.

notice it is a quadratic.

thank you!

Hi there! Don't worry, I'm here to help you out. The electric field is indeed related to the force between two charges, so you're on the right track.

To find the point where the electric field is zero, we can start by using the formula for the electric field created by a point charge:

E = k * Q / r^2

Where:
- E is the electric field strength
- k is the Coulomb's constant, approximately 9 * 10^9 Nm^2/C^2
- Q is the charge of the source (in this case, the 6 microcoulomb charge)
- r is the distance from the charge to the point where we want to find the electric field

Now, in this problem, we have a negative charge of -2.5 microcoulombs and a positive charge of 6 microcoulombs. Positive charges produce outward electric fields, while negative charges produce inward electric fields.

Since we are looking for a point where the electric field is zero, this means that the electric fields created by the two charges must be equal in magnitude but opposite in direction. Mathematically, we can express this as:

E1 = -E2

Let's now plug in the values into the equation for the electric field:

k * Q1 / r^2 = -k * Q2 / r^2

Now we can substitute the given values:
k * (-2.5 * 10^-6) / r^2 = -k * (6 * 10^-6) / r^2

The r^2 terms will cancel out, giving us:

-2.5 * 10^-6 = -6 * 10^-6

Now, we need to solve for r. Let's rearrange the equation:

r = sqrt((-2.5 * 10^-6) / (-6 * 10^-6))

Simplifying the values inside the square root, we get:

r = sqrt(2.5/6) = sqrt(5/12)

Therefore, the distance r where the electric field is zero is approximately sqrt(5/12) meters.