Two conducting spheres have identical radii. Initially thev have charges of oppo

Question

Two conducting spheres have identical radii. Initially thev have charges of opposite sign and unequal magnitudes with the magnitude of the positive charge larger than the mag- nitude of the negative charge. They attract each other with a force of 0.264 N when sepa- rated by 0.5 m. Initial The spheres are suddenly connected by a thin conducting wire, which is then removed. Connected + Now the spheres repel each other with a force of 0.041 N Final What is the magnitude of the positive charge? Answer in units of C.

Explanation / Answer

By initial condition,

F1= kq1q2/r^2

-0.264 = (9*10^9*q1q2)/0.5^2      => q1q2=- 7.33*10^-12 C^2 ----------------(1)

When they connected and removed both will have same magnitude charge , q.

q= (q1+q2)/2

By initial condition,

F2= kq^2/r^2

0.041 = [9*10^9*((q1+q2)/2)^2]/0.5^2      => q1+q2= +2.13*10^-6 C -------------(2)

Plugging (2) in (1),

q1q2= 7.33*10^-12 C^2

q1*(2.13*10^-6-q1) = 7.33*10^-12    => q1= 3.974*10^-6C or q1= -1.844*10^-6 C

Plugging this in (2) yield, q2= -1.844*10^-6 C or q2=3.974*10^-6C

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