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Question: The electrostatic force on a small sphere of charge 0.4μC due to another small sphere of charge −0.8...

The electrostatic force on a small sphere of charge 0.4μC due to another small sphere of charge −0.8μC 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?

Explanation

Solution

We can find the distance between the two spheres using Coulomb's law of electricity. The force between the two spheres is given and also the magnitude of charges on the two. So, we can find the distance between the two using Coulomb’s law. In the second part we need to find the magnitude of the force on the second sphere due to first, we can make use of Newton’s third law of motion.

Complete step by step answer:
(a) The charge on first sphere is 0.4μC0.4\mu Cand on the second sphere is −0.8μC-0.8\mu C
Therefore, q1=0.4μC=0.4×10−6C{{q}_{1}}=0.4\mu C=0.4\times {{10}^{-6}}Cand q2=−0.8μC=−0.8×10−6C{{q}_{2}}=-0.8\mu C=-0.8\times {{10}^{-6}}C
The force on one sphere due to another is given as 0.2N0.2N. Using Coulomb’s Law, we get,
F=kq1q2x2F=k\dfrac{{{q}_{1}}{{q}_{2}}}{{{x}^{2}}}, where q1{{q}_{1}} and q2{{q}_{2}} are the magnitude of the two charges and x is the distance between them. K is a constant of proportionality and its value is 9×1099\times {{10}^{9}}
⇒F=kq1q2x2\Rightarrow F=k\dfrac{{{q}_{1}}{{q}_{2}}}{{{x}^{2}}}
⇒0.2=9×109×0.4×10−6×0.8×10−6x2\Rightarrow 0.2=\dfrac{9\times {{10}^{9}}\times 0.4\times {{10}^{-6}}\times 0.8\times {{10}^{-6}}}{{{x}^{2}}}
⇒x2=9×109×0.4×10−6×0.8×10−60.2\Rightarrow {{x}^{2}}=\dfrac{9\times {{10}^{9}}\times 0.4\times {{10}^{-6}}\times 0.8\times {{10}^{-6}}}{0.2}
⇒x2=144×10−4\Rightarrow {{x}^{2}}=144\times {{10}^{-4}}
⇒x=12×10−2m\Rightarrow x=12\times {{10}^{-2}}m
∴x=0.12m\therefore x=0.12m
So, the distance between the two spheres is 0.12 m

(b) The force on the first sphere due to second was given in the question to be 0.2N0.2N and from Newton’s third law we know that forces always occurs in pair and thus the force on the second sphere due to first is also 0.2N0.2N

Note: Electric charge is the basic building block of the living and non-living substances. The smallest electric charge that could exist is the charge on the electron. Both electron and proton have the same magnitude of charge but of opposite polarity. The charge on protons is positive and the charge on electrons is negative. Both the proton and electron experience electric force. Electric charge is additive in nature and can be added using ordinary law of algebra.