Question:
The electrostatic force on a small sphere of charge 0.4 µC due to another small sphere of charge − 0.8 µC 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?
The electrostatic force on a small sphere of charge 0.4 µC due to another small sphere of charge − 0.8 µC 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?
(a) What is the distance between the two spheres?
(b) What is the force on the second sphere due to the first?
Updated On: Sep 26, 2023
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Solution and Explanation
(a) Electrostatic force on the first sphere, F = 0.2 N
Charge on this sphere, \(q_1\) = 0.4 µC = \(0.4 × 10^{−6}C\)
Charge on the second sphere, \(q_2\) = − 0.8 µC = \(− 0.8 × 10^{−6}C\)
Electrostatic force between the spheres is given by the relation
\(F = \frac{1 }{ 4πε_0}. \frac{q_1q_2}{r^2}\)
Where, \(ε_0\) = Permittivity of free space and\(\frac{1 }{ 4πε_0}\)\(= 9 × 10^9 Nm^2C^{-2}\)
Therefore,
\(r^2 = \frac{1 }{4πε0}. \frac{q_1q_2}{F}\)
\(= \frac{0.4 × 10^{-6} × 8 × 10^{-6} × 9 × 10^9 }{0.2 }= 144 × 10^{-4}\)
\(r = \sqrt{144 × 10^{ -4}} = 12 × 10^{-2} = 0.12\,m\)
The distance between the two spheres is 0.12 m.
(b) Both the spheres attract each other with the same force. Therefore, the force on the second sphere due to the first is 0.2 N.
Charge on this sphere, \(q_1\) = 0.4 µC = \(0.4 × 10^{−6}C\)
Charge on the second sphere, \(q_2\) = − 0.8 µC = \(− 0.8 × 10^{−6}C\)
Electrostatic force between the spheres is given by the relation
\(F = \frac{1 }{ 4πε_0}. \frac{q_1q_2}{r^2}\)
Where, \(ε_0\) = Permittivity of free space and\(\frac{1 }{ 4πε_0}\)\(= 9 × 10^9 Nm^2C^{-2}\)
Therefore,
\(r^2 = \frac{1 }{4πε0}. \frac{q_1q_2}{F}\)
\(= \frac{0.4 × 10^{-6} × 8 × 10^{-6} × 9 × 10^9 }{0.2 }= 144 × 10^{-4}\)
\(r = \sqrt{144 × 10^{ -4}} = 12 × 10^{-2} = 0.12\,m\)
The distance between the two spheres is 0.12 m.
(b) Both the spheres attract each other with the same force. Therefore, the force on the second sphere due to the first is 0.2 N.
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