(A) Given: Mass $m = 1 \, g = 10^{-3} \, kg$,Charge $q = 10^{-9} \, C$,Distance $x = 0.3 \, cm = 3 \times 10^{-3} \, m$,$g \approx 10 \, m/s^2$.Electr

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(A) Given: Mass $m = 1 \, g = 10^{-3} \, kg$,Charge $q = 10^{-9} \, C$,Distance $x = 0.3 \, cm = 3 \times 10^{-3} \, m$,$g \approx 10 \, m/s^2$.Electrostatic force $F_e = \frac{k q^2}{x^2} = \frac{9 \times 10^9 \times (10^{-9})^2}{(3 \times 10^{-3})^2} = \frac{9 \times 10^{-9}}{9 \times 10^{-6}} = 10^{-3} \, N$.Gravitational force $mg = 10^{-3} \times 10 = 10^{-2} \, N$.For equilibrium,$\tan \theta = \frac{F_e}{mg} = \frac{10^{-3}}{10^{-2}} = 0.1$.Therefore,$\theta = \tan^{-1}(0.1)$.

Class 12 Physics Electric Charges and Fields Electrostatic Force and Coulombs Law

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Two identical spheres,each of mass $1 \, g$,carry an identical charge of $10^{-9} \, C$. They are suspended by strings of equal length. If the distance between the centers of the spheres is $0.3 \, cm$,what is the angle made by the string with the vertical?

A
$tan^{-1}(0.1)$
B
$tan^{-1}(2)$
C
$tan^{-1}(1.5)$
D
$tan^{-1}(0.6)$

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Two identical spheres,each of mass $1 \, g$,carry an identical charge of $10^{-9} \, C$. They are suspended by strings of equal length. If the distance between the centers of the spheres is $0.3 \, cm$,what is the angle made by the string with the vertical?

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The electrostatic force on a small sphere of charge $0.4 \; \mu C$ due to another small sphere of charge $-0.8 \; \mu C$ in air is $0.2 \; N$.
$(a)$ What is the distance between the two spheres?
$(b)$ What is the force on the second sphere due to the first?