AP EAPCET 08-Jul-2022 Shift 1 Paper

The given situation is shown as;

For a system of charges potential energy is given by
U=

Σ

i=j

Kqiqj

rij

⇒ Hence for given system potential energy,
U=

Kq1q2

r12

+

Kq2q2

r13

=

K(−q)(q)

x

+

K(q)(Q)

x

+

K(−q)(Q)

√2x

=

Kq

x

(−q+Q−

Q

√2

)
So, potential energy will be zero if −q+Q−

Q

√2

=0
or Q(1−

1

√2

)=q
⇒ Q=(√2−1)=√2q
⇒ Q=

√2q

√2−1