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How can we take an infinitesimal amount of a point charge of charge $q$? Doesn't infinitesimal charge means the smallest object?What could be smaller than a point?

YouTube: JEE ADVANCED | ORIGINALS | DIPOLE BETWEEN CONDUCTING PLATES |INDUCED CHARGE | ELECTROSTATICS

The same thing has been done here. First they thought of dividing the point charge $q$ into many infinitesimal charges but i don't find it intuitive.

GrapefruitIsAwesome
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green_blue
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2 Answers2

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He is not making the charge spatially smaller. As you say, a point charge is already as small as possible in terms of spatial extent.

He is instead making the charge weaker. Classically you could have a point charge of $q$ or a point charge of the same spatial size but a stronger charge, say $2 q$. Or a weaker charge $q/2$ or $q/3$ or $q/4$ or … $q/n$. As $n$ becomes infinite $dq$ becomes an infinitesimally weak point charge.

Dale
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  • But according to him,the sum of all those infinitesimal charges should amount to $q$ and he means that those $dq$, charges are part of that point charge $q$ since we are calculating lines of field of $q$ charge using $dq$ charges. – green_blue Feb 13 '22 at 22:26
  • @green_blue See: Infinitesimal "In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished from zero by any available means. ... An infinite number infinitesimals are summed to calculate an integral." – GrapefruitIsAwesome Feb 13 '22 at 22:30
  • @green-blue no, he does not mean that they are part of $q$, just that the total amount of charge of all the $dq$ is equal to $q$. He is not saying that one is formed from another, he is just restructuring the problem in an easier way. He is not saying that the mathematical operation is a physical one. – Dale Feb 13 '22 at 23:22
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I wasn't able to watch the video, but the most "infinitesimal" amount of charge possible is the charge on one electron or proton. 1 coulomb of charge is the charge of 6.24 x 10$^{18}$ electrons or protons. In other words, the smallest known quantity of electricity, or "elementary charge" is 1.602 x 10$^{-19}$ coulombs.

Hope this helps.

Bob D
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