QJEEM13Phbcb7: JEE Main 2013 Physics - Class 12 JEEM13Phbcb7 Solution: Two charges, each equals to q , are kept at x = − a and x = a…

Question

Verified Solution • 2025–26 Session moderate

Two charges, each equals to

q,

are kept at

x = - a

and

x = a

on the

x

-axis. A particle of mass

m

and charge

q_{0} = \frac{q}{2}

is placed at the origin. If charge

q_{0}

is given a small displacement

(y << a)

along the

y

-axis, the net force acting on the particle is proportional to

Accepted Answer

\Rightarrow F_{n e t} = 2 F \cos θ

F_{n e t} = \frac{2 k q (\frac{q}{2})}{{(\sqrt{y^{2} + a^{2}})}^{2}} . \frac{y}{\sqrt{y^{2} + a^{2}}}

F_{n e t} = \frac{2 k q (\frac{q}{2}) y}{{(y^{2} + a^{2})}^{3 / 2}} \Rightarrow \frac{k q^{2} y}{a^{3}}

S0,

F \propto y

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