The figure at the right shows a small positive charge some distance away from a

Question

The figure at the right shows a small positive charge some distance away from a larger positive charge. The smaller charge is currently a distance r_1 away from the center of the larger charge, which is twice as far away as r_2 Answer the three questions below, using three significant digits. What happens to the potential energy and the force if the smaller charge is moved to r_2? Both the force and the potential energy decrease. Both the force and the potential energy increase. The force increases, but the potential energy decreases. The force decreases, but the potential energy increases. Neither the force nor the potential energy change. Suppose that there is a force of 0.0123 N when the smaller charge is at r_1. What is the value of the force (F_2) when the charge is moved to r_2? F_2 = Suppose that the potential energy is 5.77 times 10^-3 J when the smaller charge is at r_1. What is the value of the potential energy (U_2) when the charge is moved to r_2?

Explanation / Answer

part A :

Potential Energy Due to two charges is given by

U = Kq1q2/r

And Force is given by F = Kq1q2/r^2

as the charge is Brought Closer to another charge

Distance between them decreases

thus Force and PE increases

option two

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F1 = Kq1q2/r1^2

F2 = Kq1q2/r2^2

F2/F1 = r1^2/r2^2

here r1 = 2 r2

F2/F1 = 4 r2^2/r2^2 = 4

so

F2 = 4* 0.0123   

F2 = 0.0492 N

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U2/U1 = r1/r2

U2 = U1 * 2 r2/r2 =

U2 = 5.77 *10^-3 * 2

U2 = 11.54 *10^-3 J

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