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Two point charges (Q each are placed at ...

Two point charges (Q each are placed at (0,y) and (0-y) A point charge q of the sme polarity can move along the x-axis. Then

A

the force on q is maximum at `x=+-y//sqrt(2)`

B

the charge q is in equilibrium at the origin

C

the charge q performs an oscillatory motion about the origin

D

for any position of q other than origin the force is directed away from origin

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Net force on q
`F_("net")=2F cos theta =(2)/(4 pi epsilon_(0))(Qq)/((x^(2)+y^(2))) (x)/(sqrt(x^(2)+y^(2)))`
`(Qq)/(2 pi epsilon_(0)) (x)/((x^(2)+y^(2))^(3//2))`

To maximize `F_("net")`
`(dF_("net"))/(dx)=0 or x =+-(y)/(sqrt(2))`. Hence (a) is correct.
At origin x=0 `F_("net")=0`. Hence (b) is correct. since net force is away form origin particle will not perform oscillatory motion. Hence (c ) is incorrect and (d) is correct.
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