A small metal sphere, carrying a net charge of q 1 = -2.60 ? C , is held in a st

Question

A small metal sphere, carrying a net charge of q1 = -2.60 ?C , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.70 ?C and mass 1.80 g , is projected toward q1. When the two spheres are 0.800m apart, q2 is moving toward q1 with speed 22.0 m/s (Figure 1) . Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

a) What is the speed of q2 when the spheres are 0.450 m apart?

b)How close does q2 get to q1?

Explanation / Answer

We know that total energy of the system equals to sum of kinetic energy and potential energy i.e is E=U+K.E

Where U=kq1q2/r

            where k=8.99*10^9nm^2/c^2

given q1=-2.60*10^-6c and q2=-7.70*10^-6c

by calculating we get U=0.224j

then kinetic energy K.E=(mv^2)/2

given m=1.80g and velocity v=22.0m/s

K.E=0.4356j

then total energy is U+K.E

=0.6596J

(1)

given at r=0.45m

then 0.6596=kq1q2/r+(mv^2)/2

at here by substitute above values we get velocity V as 17.12m/s

(2)

E=kq1q2/r

therefore r=8.89*10^9*2.6*7.7*10^-12/0.6596

hence we get distance r=0.269m

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