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Two point charges q(1)=-4muC and q(2)=8m...

Two point charges `q_(1)=-4muC and q_(2)=8muC` are lying on the y-axis. They are equidistant from the point P, which lies on the x-axis. A small object of charge `q_(0)=8muC` and mass m = 12 g is placed at P. When it is released, which is its acceleration in `ms^(-2)`?
(Neglect the effect of gravity)

A

`3sqrt3hati+9hatj`

B

`9hati+3sqrt3hatj`

C

`3hati+3sqrt3hatj`

D

`3sqrt3hati+3hatj`

Text Solution

Verified by Experts

The correct Answer is:
A
`|F_(1)|=|(9xx10^(9)xx(-4)xx8xx10^(-12))/((2)^(2))|=72xx10^(-3)N`
`|F_(2)|=(9xx10^(9)xx8xx8xx10^(-12))/((2)^(2))=144xx10^(-3)N`

`f_(y)=F_(1)sin30^(@)+F_(2)sin30^(@)=108xx10^(-3)N`
`f_(x)=F_(2)cos30^(@)-F_(1)sin30^(@)=36sqrt3xx10^(-3)N`
`F=f_(x)hati+f_(y)hatjorvecF=36sqrt3xx10^(-3)hati+108xx10^(-3)hatj`
`m=12g=12xx10^(-3)kg`
`veca=(vecF)/m=((36sqrt3hati+108hatj)xx10^(-3))/(12xx10^(-3))=3sqrt3hati+9hatj`
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