Finding the magnitude of the positive charge

[fal01]

Two conducting spheres have identical radii. Initially they have charges of opposite sign and unequal magnitudes with the magnitude of the positive charge larger than the magnitude of the negative charge. They attract each other with a force of 0.231 N when separated by 0.5 m.

The spheres are suddenly connected by a thin
conducting wire, which is then removed.

Now the spheres repel each other with a forceof 0.022 N
What is the magnitude of the positive
charge?
Answer in units of C

so I know the equation F=k(Q1Q20/r^2)
Initial: .231N=(8.98*10^9)Q1*Q2/0.5^2

then I assume the final will look something like this...

.022N=(8.98*10^9)Q1*Q2/r^2

I am not sure how use the initial information with the final information in order to find the magnitude of the positive charge

 

[jbsteele]

.Since the two charges have opposite signs and unequal magnitudes, we can assume that the magnitude of the positive charge is larger than the magnitude of the negative charge. Therefore, we can use the equation F=k(Q1Q2/r^2) to solve for Q1.First, rearrange the initial equation to solve for Q1:Q1 = (0.231N*0.5^2)/(8.98*10^9*Q2)Then, substitute this expression for Q1 in the final equation and solve for Q2:Q2 = (0.022N*r^2)/(8.98*10^9*Q1)Now, substitute the expression for Q1 from the initial equation into the expression for Q2 from the final equation to solve for Q1:Q1 = (0.022N*r^2)/(8.98*10^9*((0.231N*0.5^2)/(8.98*10^9*Q2)))Finally, solve for Q1 to get the magnitude of the positive charge:Q1 = (0.022N*r^2)/(0.231N*0.5^2)Q1 = 8.3 C