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Good evening Eshan sir... This is yester day solution sir. How sir electric field is independent r. Generally E = (1/4π€0) (Q/r^2). I did not understand explain sir.

Good evening Eshan sir...
This is yester day solution sir.
How sir electric field is independent r.
Generally E = (1/4π€0) (Q/r^2).
I did not understand explain sir.

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1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear Raju,

It is not true that electric field always follows the relationE=\dfrac{1}{4\pi\epsilon_0}\dfrac{Q}{r^2}. This is true only for electric field due to a point charge, or due to a uniformly charged solid sphere or spherical shell. In fact electric field due to an infinitely large charged conducting plate with charge per unit area\sigmais\dfrac{\sigma }{2\epsilon_0}which is also independent ofr. In case of infinitely large wire, it is\dfrac{\lambda}{2\pi\epsilon_0 r} Hence it depends upon the distribution of charges in the given situation.


Here we are asked about the value of ‘A’ such that electric field is independent ofr. Using the Gauss law, we arrived at an expression of electric field in terms ofr. Now this has a constant term in addition to a term having dependence as\dfrac{1}{r^2}. But it is given that field must be independent ofr. So if the coefficient of this\dfrac{1}{r^2}term becomes zero, then the electric field would only have the magnitude\dfrac{A}{2\epsilon_0}. Hence we have put it to zero to find the value of ‘A’.

Hope that helps.

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