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Positive charge Q is uniformly distribut...

Positive charge Q is uniformly distributed throughout the volume of a sphere of radius R. A Point mass having charge `+q` and mass m is fired towards the centre of the sphere with velocity v from a point A at distance `r(r gt R)` from the centre of the sphere. Find the minimum, so that it can penetrate R/2 distance of the sphere. Neglect any resistance other than:e-c141::, interaction. Charge on the small mass remains constant throughout the motion

Text Solution

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`(1)/(2)mv^(2)+(Qq)/(4piepsilon_(0))*(1)/(r )=(Qq)/(4pi_(0))[(3R^(2)-(R//2)^(2))/(2R^(3))]=(Qq)/(4pi)[(11R^(2))/(8R^(3))]=(11Qq)/(32piepsilon_(0)R)`
`v^(2)=(2)/(m)[(11Qq)/(32piepsilon_(0)R)-(Qq)/(4piepsilon_(0))*(1)/(r )]`
`rArr v=sqrt((11Qq)/(16piepsilon_(0)Rm)-(Qq)/(2piepsilon_(0))(1)/(mr))`
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