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NEET 2013
Exam
NEET
Year
2013
Subject
Physics
Chapter
Electrostatics

NEET 2013 · Physics · Electrostatics

A charge ' q ' is placed at the centre of the line joining two...

A charge ' qq ' is placed at the centre of the line joining two equal charges ' QQ '. The system of three charges will be in equilibrium if ' qq ' is equal to:A charge ' q ' is placed at the centre of the line joining two equal charges ' Q '. The system of three charges will beA charge ' q ' is placed at the centre of the line joining two equal charges ' Q '. The system of three charges will be

Options

  1. A−Q/4-Q / 4
  2. BQ/4Q / 4
  3. C−Q/2-Q / 2
  4. DQ/2Q / 2

Correct answer

A. −Q/4-Q / 4

Step-by-step solution

 According to  the  question  \text{ According\text{ to }\text{ the }\text{ question } }A charge ' q ' is placed at the centre of the line joining two equal charges ' Q '. The system of three charges will be \\ for equilibrium, net force on charge Q=0\quad Q=0 \therefore 14πϵ0Qqr2+14πϵ0⋅Q2σ(r2)2=\frac{1}{4 \pi \epsilon_0} \frac{\mathrm{Qq}}{r^2}+\frac{1}{4 \pi \epsilon_0} \cdot \frac{\mathrm{Q}^2}{\sigma\left(\frac{r}{2}\right)^2}=0 ⇒14πϵ0Q2r2=−14πϵ04Qqr2⇒Q=−4q⇒q=−Q4\begin{aligned} \Rightarrow& & \frac{1}{4 \pi \epsilon_0} \frac{\mathrm{Q}_2}{r^2}& =-\frac{1}{4 \pi \epsilon_0} \frac{4 \mathrm{Q} q}{r^2}\\ \Rightarrow & & Q & =-4 q \\ \Rightarrow & & q & =-\frac{Q}{4} \end{aligned}
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