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Electric Charges and Fields — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields5 Marks
Question
Consider the situation of the previous problem:
  1. Find the tension in the string in equilibrium.
  2. Suppose the ball is slightly pushed aside and released. Find the time period of the small oscillations.
✓

Answer


In equilibrium state, the thread makes an angle of $60^\circ$ with the vertical.
The tension in the thread is resolved into horizontal and vertical components.
Then, tension in the string in equilibrium,
$\text{T}\cos60^\circ=\text{mg}$
$\text{T}\times\frac{1}{2}=\big(10\times10^{-3}\big)\times10$
$\text{T}=\big(10\times10^{-3}\big)\times10\times2=0.20\text{N}$
$(b)$ As it is displaced from equilibrium, net force on the ball,
$\text{F}=\sqrt{(\text{mg})^2+\Big(\frac{\text{q}\sigma}{2\epsilon_0}\Big)^2}$
As $F = ma$
$\Rightarrow\text{a}=\sqrt{(\text{g})^2+\Big(\frac{\text{q}\sigma}{m2\epsilon_0}\Big)^2}$
The surface charge density of the plate $($as calculated in the previous question$),$
$\sigma=7.5\times10^{-7}\text{C/m}^2$
Charge on the ball, $q = 4 \times 10^{-6}C$
Mass of the ball $, m = $The time period of oscillation of the given simple pendulum,
$\text{T}=2\pi\sqrt{\frac{\text{l}}{\text{g}}}$
$=2\pi\sqrt{\frac{10\times10^{-2}}{9.8}}$
$=0.45\text{ sec}$

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