A) What is the magnitude of the positive charge? Answer in units of C. B) What i

Question

A) What is the magnitude of the positive charge? Answer in units of C.

B) What is the negative charge? Answer in units of C.

022 (part 1 of 2) 10.0 points 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 mag- nitude of the negative charge. They attract each other with a force of 0.22 N when sepa- rated by 0.3 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 0.031 N. Final + What is the magnitude of the positive charge? Answer in units of C 023 (part 2 of 2) 10.0 points What is the negative charge? Answer in units of C

Explanation / Answer

First case

So k*q1*q2/r^2 = F

or 9.0x10^9*q1*q2/0.30^2 = 0.139

therefore q1*q2 = 1.39x10^-12

in the second case the charges (q) are equal and they equal (q1 - q2)/2

so k*q^2/r^2 = 0.022

so q = sqrt(0.022*0.3^2/9.0x10^9) = 4.69x10^-7

therefore q2 = q1 - 2*q

plugging this into the first eqn above we get

q1*(q1 - 2*4.69x10^-7) = 1.39x10^-12

or q1^2 - 9.38x10^-7*q1 - 1.39x10^-12 = 0

so q1 =1.74x10^-6C

b) so q2 = q1 - 2*q = 1.74x10^-6 - 4.69x10^-7 = 7.58x10^-7C

(Since it was assumed to be negative we have -7.58x10^-7C )

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