Two identical conducting spheres, fixed in place, attract each other with a forc

Question

Two identical conducting spheres, fixed in place, attract each other with a force of 0.112 N when their center to center separation is 49.00 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres have a net positive charge and repel each other with an electrostatic force of 0.038 N. What was the initial negative charge on one of the spheres, and what was the initial positive charge on the other?(Hint: Use charge conservation and solve for one of the initial charges. You will end up with a quadratic equation. The solutions give you the positive and negative charges.)

Initial negative charge (Need answer)
Initial positive charge (Need answer)

please show thoroughly and write answers.

Explanation / Answer

call the magnitude of the charges Q and q where q is the negativecharge

then initialforce: F = k Q q /r^2

0.112 = k Q q / 0.49^2

Now the total charge will be C suchthat C = Q - q

you know each sphere gets C/2 after they touched so

final force: 0.038 = k (C/2) (C/2) /0.49^2

So now, simplify the expressions

0.027 = k Qq 0.036495 = k C^2

use 8.99 x 10^9 for k and

3.00 x 10^-12 = Qq

4.055 x 10^-9 = C^2

Q = 3.00 x 10-12 /q to make thissimpler, Q = a / q wherea is that number

also b =C^2 where b = 4.055 ...

Now

b = ( Q - q)^2 b = (a/q - q )^2

vb = a/q - q

q vb = a - q2

you have a quadratic in q 0 = q2 + vb q - a

using quadratic formula you get

q = ( -vb +/- ( b +4a)1/2 ) / 2

Plug in the numbers and you get

plug in numbers to get two charges

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