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0 votes
6.3k views
in Electrostatics by (20 points)
reopened by

A point charge Q of mass m is projected with some initial velocity v from a very far off point as shown. The sphere shown has a charge –Q, radius R and charge is uniformly distributed over its entire volume. Through out the process, this sphere stays stationary. Find v so that the point charge strikes the sphere at 45°. (given that α = Image not present, g=0)

                                                                         Image not present

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1 Answer

–1 vote
by (16 points)

​Apply energy conservation

1/2mv2 + 0 = -kQ2/R + 1/2mV2

Now since there is only electrostatic force between them so the net force always pass through the line joining their centres hence the torque about centre of sphere =0 so angular momentum is conserved about this point

According to conservation of momentum

=mv(2R)=mVR

or V=2v 

Substitute this in first eqn and use the value of alpha given in the question we get 

v=\(\sqrt \frac{2\alpha}{3}\)

by (20 points)
edited by
+1
Great answer, however you forgot to take into account that the point charge will strike the sphere at 45°.
Therefore when conserving momentum-
mv(2R)=\(mVR \over \sqrt{ 2}\)

or V=\(2\sqrt{2}\)v

Hence, v= \(\sqrt{2α \over 7}\)
by (15 points)
saarthak.batra your answer is actually the correct answer.

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