# Equivalent Electri Force, Find the charge.

## Homework Statement

Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.3 m. In a vacuum, each object carries a different charge, and they attract each other with a force of 2.3 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object? (Note: there are two possible pairs of answers, but assume q1 to be the larger number.)

F=kq1q2/r2

## The Attempt at a Solution

So I know that since force is equal Fr2/k is a constant. Also since the charge in the 2nd case is equally shared I can re-write the equation for force as F=kq2/r2. Solving for q gets me 4.8e-6.

From here since the charge was shared equally between q1 and q2, q=q1+q2/2. Using substitution to solve for q2, I came up with the following quadratic:

-q12+9.6e-6(q1)-9.6e-6. This results in an invalid quadratic equation because b2-4ac gives me a negative number. I think I made math errors or I'm missing a step, but the underlying concept makes sense.

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.3 m. In a vacuum, each object carries a different charge, and they attract each other with a force of 2.3 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object? (Note: there are two possible pairs of answers, but assume q1 to be the larger number.)

F=kq1q2/r2

## The Attempt at a Solution

So I know that since force is equal Fr2/k is a constant. Also since the charge in the 2nd case is equally shared I can re-write the equation for force as F=kq2/r2. Solving for q gets me 4.8e-6.

From here since the charge was shared equally between q1 and q2, q=q1+q2/2. Using substitution to solve for q2, I came up with the following quadratic:
Be careful with parentheses. That should be written,
q = (q1+q2)/2​
-q12+9.6e-6(q1)-9.6e-6. This results in an invalid quadratic equation because b2-4ac gives me a negative number. I think I made math errors or I'm missing a step, but the underlying concept makes sense.

It's likely that the signs of the charges is what's causing your problems.

The magnitude of the force is the same for both situations, so
|q1q2| = q2
but because q1q2 is negative,
|q1q2| = -q1q2 .​

ok now I just got a completely wrong answer. My new quadratic equation is q22-9.59e-6+4.8e-6. I got answer of like .00348

SammyS
Staff Emeritus