Three charges $+\mathrm{Q}, \mathrm{q},+\mathrm{Q}$ are placed respectively, at distance, $0, \mathrm{~d} / 2$ and d from the origin, on the $x$-axis. If the net force experienced by $+Q$, placed at $x=0$, is zero, then value of $q$ is

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Electrostatics

Three charges

+ Q, q, + Q

are placed respectively, at distance,

0, d /2

and d from the origin, on the

x

-axis. If the net force experienced by

+ Q

, placed at

x = 0

, is zero, then value of

q

Answer: (A)

The

+ Q

at the origin feels two pushes along the

x

-axis, one from the middle charge

q

\frac{d}{2}

and one from the

+ Q

d

. For the net force to vanish these must cancel, so their magnitudes match:

\frac{k Q ∣ q ∣}{( d /2 ) ^{2}} = \frac{k Q ^{2}}{d ^{2}}

, that is

\frac{4 k Q ∣ q ∣}{d ^{2}} = \frac{k Q ^{2}}{d ^{2}}

, giving

∣ q ∣ = \frac{Q}{4}

. Since the far

+ Q

repels the origin charge outward, the middle charge must pull it back the other way, so

q

has to be negative,

q = - \frac{Q}{4}

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option