(a) Calculate the potential energy of a system of two small spheres, one carryin

Question

(a) Calculate the potential energy of a system of two small spheres, one carrying a charge of 2.31 µC and the other a charge of -3.80 µC with their centers separated by a distance of 0.250 m. Assume zero potential energy when the charges are infinitely separated.
J

(b) Suppose that one of the spheres is held in place and the other sphere, which has a mass of 1.50 g is shot away from it. What minimum initial speed would the moving sphere need in order to escape completely from the attraction of the fixed sphere? (To escape, the moving sphere would have to reach a velocity of zero when it was infinitely distant from the fixed sphere.)
m/s

Explanation / Answer

(a)

Potential energy of two spheres.

U=k*q1*q2 /r

where, r is distance btween two spheres.

Here, spheres are assumed to be point charge, and it resonable assumption.

U=9*10^9*2.31*10^-6*(-3.80*10^-6)/0.250

=-0.316 J.

(b) @ infinite distance, total energy of the system will be zero.

So we need to give exactly kinetic energy to the potential energy of the system.

E=P.E. + K.E. = 0 @ infinite distance

1/2*m*v^2 - 0.316 = 0

v^2 = 0.316*2/1.5*10^-3

=421

v= 20.51 m/s

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