A pendulum bob having a mass of 80 mg and carrying a charge of 2 ×...

Given, mass of the bob, $m = 80 \text{ mg} = 80 \times 10^{-6} \text{ kg}$

Charge on the bob, $q = 2 \times 10^{-8} \text{ C}$

Electric field, $E = 20 \text{ kV m}^{-1} = 2 \times 10^{4} \text{ V m}^{-1}$

The electric force acting on the bob horizontally is:

$F_{e} = qE = (2 \times 10^{-8} \text{ C})(2 \times 10^{4} \text{ V m}^{-1}) = 4 \times 10^{-4} \text{ N}$

The gravitational force acting on the bob vertically downwards is:

$W = mg = (80 \times 10^{-6} \text{ kg})(9.8 \text{ m s}^{-2}) = 7.84 \times 10^{-4} \text{ N}$

Since the bob is at rest, the tension $T$ in the thread balances the resultant of the electric force and the weight. Since $F_{e}$ and $W$ are perpendicular to each other, the tension is given by:

$T = \sqrt{F_{e}^2 + W^2}$

Substituting the values:

$T = \sqrt{(4 \times 10^{-4})^2 + (7.84 \times 10^{-4})^2}$

$T = 10^{-4} \sqrt{16 + 61.4656}$

$T = 10^{-4} \sqrt{77.4656}$

$T \approx 8.8 \times 10^{-4} \text{ N}$