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Two point positive charges q each are pl...

Two point positive charges q each are placed at `(-a,0) and (a,0)`. A third charge `q_(0)` is placed at `(0,y)`. For which value of y the force at `q_(0)` is maximum …………………

A

a

B

2a

C

`(a)/(sqrt(2))`

D

`(a)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
C

`F_(1)=(kq_(0)q)/((a^(2)+y^(2))),F_(2)=(kq_(0)q)/((a^(2)+y^(2))), therefore F_(1)=F_(2)`
Resultant `F=2F_(1)costheta=(2kqq_(0))/(a^(2)+y^(2))(y)/(sqrt(a^(2)+y^(2))),` Force on `q_(0)` will be maximum, when `(dF)/(dy)=0`
`therefore 2kqq_(0)[(1)/((a^(2)+y^(2))^(3//2))-(((3)/(2)y)(2y))/((a^(2)+y^(2))^(5//2))]=0 therefore (1)/((a^(2)+y^(2))^(3//2))-(3y^(2))/((a^(2)+y^(2))^(5//2))=0`
`a^(2)+y^(2)=3y^(2), a^(2)=2y^(2), impliesy=(a)/(sqrt(2))`
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