Q128 / 180 · JIPMER 2015 · Physics

Two small balls, each carrying a charge $q$ are suspended by equal insulator strings of length 1 m from the hook of a stand. This arrangement is carried in a satellite in space. The tension in each string will be

  • A
    $\frac{1}{4 \pi \varepsilon_0} \frac{q}{l^2}$
  • Correct answer
    B
    $\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{4 l^2}$
  • C
    $\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{l^2}$
  • D
    $\frac{1}{\left(4 \pi \varepsilon_0\right)} \frac{q}{l}$

Solution

Suppose, $T$ be the tension in the spring $T$. Also in the satellite, two balls will be in a straight line. So, force acting on the balls $F=\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{(2 l)^2}$ $\ldots$ (i) This force will be balanced by tension in the string. i.e., $T=F$ $\ldots$ (ii) Now, from Eqs. (i) and (ii), we get $T=\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{4 l^2}$

Hence, the correct answer is option: 'B'.

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