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Sketch the variation of electric circle potential on the x-axis with respect to x for x = - oo to x = + oo in the following cases. (a) |
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Answer» Solution :(a) Electric potential at `P` : `V_(p) = (1)/( 4pi in_(0)).[(Q)/(x) + (Q)/(d - x)] = (Q)/(4 pi in_(0)) .(d)/(x(d - x))` `V_(p)` is minimum if `x(d - x)` is maximum. `x(d - x)` is maximum if `x = d - x rArr x = d//2`. At mid -point of `OA` , electric potential is minimum. At `O : x rarr 0 ,V rarr oo` At `A : x rarr d , V rarr oo` From `O` to `A` , electric potential decreases REACHING to minimum VALUE and then increases. Left of `O` : At DISTANCE `x` from `O` `V = (1)/( 4 pi in_(0)) [(Q)/(x) + (Q)/(d + x)]` `x rarr 0 , V rarr oo` `x rarr -oo , V rarr 0` Right of `A` : At distance `x` from `O` `V = (1)/(4pi in_(0)) [(Q)/(x) + (Q)/(x - d)]` `x rarr d , V rarr oo` `x rarr oo , V rarr 0` (B) At mid - point of `OA , V = 0` `0 lt x lt (d)/(2) , V is + ve` `(d)/(2) lt x lt d , V is - ve` `x rarr 0 , V rarr oo` `x rarr 0 , V rarr oo` `x rarr -oo , Vrarr 0` Right of `A : V is -ve` `x rarr d , V rarr oo` `x rarr oo , V rarr 0`   
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