Two identical conducting spheres are separated by a fixed center-to-center dista

Question

Two identical conducting spheres are separated by a fixed center-to-center distance of 43 cm and have different charges. Initially, the spheres attract each other with a force of 0.095 N. The spheres are now connected by a thin conducting wire. After the wire is removed, the spheres are positively charged and repel one another with a force of 0.032 N. Find (a) the final and (b) the initial charges on the spheres.

Part A

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

Part B

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

Explanation / Answer

Force of attraction = k . Q1 . Q2 / 0.43^2

After they are connected, charge on each will be the same

F = k . Q(new)^2 / 0.43^2

Q (new) = 0.032 . 0.43^2 / 9 . 10^9 = 8.108x10^–7 C

(b) |Q1 – Q2| / 2 = 8.108 x10^–7

Q1 – Q2 = 16.216x 10^–7 C

( the two charges partly cancel each other and then share whatever charge is left )

0.095 = 9 . 10^9 . Q1 . Q2 / 0.47^2

2.332 . 10^–12 = Q1 . Q2

You have to substitute Q2 = Q1 – 16.216 x 10^–7

2.332 . 10^–12 = Q1 .(Q1 – 16.216 x 10^–7 )

Q1=2.539x10^-6C , -9.182x10^-7C

Q2=9.174x10^-7C ,-2.5396x10^-6

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