Calculate Charge on Each Sphere: Force and Total Charge Given

[jmb07]

total charge of 6.63E-6 C distributed on 2 metal spheres. When the spheres are 6 cm apart, they each feel a repulsive force of 26.9 N. How much charge is on each sphere??

I know that F=(k x q1 x q2)/(r x r)

Im not exactly how to solve for these when i don't know either one of them to solve for one another. How should i go about this??

 

[exitwound]

You can use the fact that q1+q2=6.63E-6. Use it as your second equation.

 

[jmb07]

how would i relate q1 to q2? Like i understand that the two added together is the total charge.
Should i say that q2 = (F rxr)/(k x q1)
and q1 = 6.63E-6 - q2

I try plugging the relations in but i can't seem to put it all together for some reason

 

[exitwound]

If
$$Q_1+Q_2=6.63e^{-6}$$,

then
$$Q_1=6.63e^{-6} - Q_2$$

Substituting that back into your Force equation:

$$F=k\frac{(Q_1)(Q_2)}{r^2}$$

$$F=k\frac{(6.63e^{-6} - Q_2)(Q_2)}{r^2}$$

Solve for Q_2. In this way, you have used the value of Q2 to state the value of Q1 and your equation is then only dependent on the one variable, Q2, instead of two. After finding Q2, you should be able to figure out Q1 in one step.

 

[jmb07]

thanks! I think i am having an algebra block though haha. So,
(6.63E-6 - q2)(q2) = (Frxr)/k

Do i need to use the quadratic equation to solve for q2 or is there a more simple way i am missing?

 

[queenofbabes]

It appears to be unavoidable. It's not exactly difficult =)