Where Should a -3 MicroCoulomb Charge Be Placed to Achieve Zero Net Force?

[creeps228]

Homework Statement

Two charges are separated as shown. Where would you place a -3 microCoulombs (mC) charge such that the net force on this charge is 0?

+ +
4mC 8mC
Distance between charges are 80cm apart.

Homework Equations

F= (k*q1*q2) / (r*r)

The Attempt at a Solution

I found out the Force on q1 ( i made q1 the 4mC charge and q2 the 8mC charger) to q2
it came to be 4.5*10^(-1) N. Same for the F for q2 on q1. Then i manipluated the equation to slove for r. Once that was established i but the -3mC charge in the equation with the 4mC charge and F being 4.5*10^(-1) giving me an approximation of .5m aka 50 cm. But that doesn't seem right, what equation I am not using to get this answer?

 

[christensen]

Because the net force acting on the charge is 0N, we know that the electric field is 0 N/C.

Now, through simple arguments we know the point we are looking for is inbetween the two charges and that the field strength from charge 1 has to equal the field strength from charge 2 (in magnitude).

*Let a be the distance from q₁ to the point of E = 0 and b be the distance from q₂ to the point of E = 0.

So, E₁ = E₂

k*q₁/a² = k*q₂/b²

Cancel k to get,

q₁/a² = q₂/b²

you can reorganize the equation to be simplier to use later on to,

q₁*b² = q₂*a²

Now you also have a + b = 80cm

By substituting into another, you can solve for a or b, and thus solve for the other, giving you the point in which there is zero force on the charge.

 

[creeps228]

I subsituted b for 80-a

so using the equation you gave q1= 4mC q2=8mC

4mC*[(80-a)^2] = 8mC*[a^2]
= 4mC* (6400-160a+[a^2]) = 8mC*a^2

which seems more confusing then just doing problem itself

 

[christensen]

you now have a simple equation to solve for the value of "a"

4mC* (6400-160a+[a^2]) = 8mC*a^2
(6400-160a+[a^2]) = 2*a^2
6400 = a^2 + 160a

a = 33.137 (approx)

so the charge must be placed 33.137cm from the 4mC charge.

 

[creeps228]

Thankyou. The force of the 3mC charge from the other two chargers were about .02 difference. Basically one was 9.7*10^(-11) and the other was 9.9*10^(-11). Close to zero as possible, but thankyou.