Question

Two small spheres each having equal position charge $Q$ (Coulomb) on each are suspended by two insulating strings of equal length $L$ (meter) from a rigid hook (shown in Fig). The whole set up is taken into satellite where there is no gravity. The two balls are now held by electrostatic forces in horizontal position, the tension in each string is:

• A. $\frac{Q^2}{16\pi {\epsilon }_o{L}^2}$
• B. $\frac{Q^2}{8\pi {\epsilon }_o{L}^2}$
• C. $\frac{Q^2}{4\pi {\epsilon }_o{L}^2}$
• D. $\frac{Q^2}{2\pi {\epsilon }_o{L}^2}$

Answer 1

The correct option is A $\frac{Q^2}{16\pi {\epsilon }_o{L}^2}$

In this case, both the charges will repel each other and distance between the two will become $2L$.

Hence, balancing forces on any one sphere, we get,

$T=\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{{\left(2L\right)}^2}=\frac{Q^2}{16\pi {ϵ}_0{L}^2}$