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A ball of mass 2Kg charge 1muC is droppe...

A ball of mass `2Kg` charge `1muC` is dropped from top of a high tower.In space electric field exists in horizontal direction away from the tower which varies as
`E=(5xx2x)xx10^(6)Vm(-1)` .Find maximum horizontal distance that the ball can go from the tower.

Text Solution

Verified by Experts

The correct Answer is:
5
`a_(x)=(qE)/(m)rArr (dv_(x))/(dt)=(q)/(m)(5-ax)`
`At underset(vdownarrow)("time t") rarr
E=(5-2x)xx10^(6)rArr v(dv)/(dx)=(q)/(m)(5-2x)`
`(V_(x)^(2))/(2) =(q)/(m)(5x-x^(2))rArr v_(x)^(2)=(2q)/(m)(5x-x^(2))`
` rArr (dx)/(dt)=sqrt((2q)/(m)(5x-x^(2)))` for `x` to be maximum
`(dx)/(dt)=0rArr 5x-x^(2)=0rArr x=5m`
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