Two balls of charge q₁ and q₂ initially have a velocity of the same magnitude and direction. After a uniform electric field has been applied during a certain time, the direction of the velocity of the first ball changes by 60^ , and the velocity magnitude is reduced by half. The direction of the velocity of the second ball changes thereby by 90^ . In what proportion will the velocity of the second ball change? Determ

Step-by-step solution

Let v₁ and v₂ be the velocities of the first and second balls after the removal of the uniform electric field. By hypothesis, the angle between the velocity v₁ and the initial velocity v is 60^ . Therefore, the change in the momentum of the first ball is p₁=q₁ E t=m₁ v 60^ Here we use the condition that v₁=v / 2 , which implies that the change in the momentum p ₁ of the first ball occurs in a direction perpendicular to the direction of its velocity v₁ . Since E | p ₁ and the direction of variation of the second bal