Question

Two small balls, each carrying a charge q are suspended by equal insulator string of length $\frac{l}{2}$ m from the hook of a stand. This arrangement is carried in a satellite in space. The tension in each string will be :

• A. $\frac{1}{4\pi {\epsilon }_0}\frac{q}{l^2}$
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{4l^2}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{l^2}$
• D. $\frac{1}{\left(4\pi {\epsilon }_0\right)}\frac{q}{l}$

Answer 1

The correct option is C $\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{l^2}$

As we know that there is no gravity in space. Thus no gravitational force acts on the ball in the downward direction.

In space, the only forces acting on a charge are the tension of the spring (upwards) and the electrostatic force which are balanced.

Thus, tension in the string $T=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{l^2}$