sing the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius Rand total charge Q) at xg distance from its center? (Consider that the surface of the late lies in the yz plane) olution perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. here will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. o for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E- (1/ since, the actual ring (whose charge is da) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ Ve wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E= (x0/ valuating the integral will lead us to QXo 1 1 E- 4 TEGR Xo (x3 + R²)/2 ibetituriner
sing the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius Rand total charge Q) at xg distance from its center? (Consider that the surface of the late lies in the yz plane) olution perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. here will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. o for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E- (1/ since, the actual ring (whose charge is da) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ Ve wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E= (x0/ valuating the integral will lead us to QXo 1 1 E- 4 TEGR Xo (x3 + R²)/2 ibetituriner
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Transcribed Image Text:Problem
Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius Rand total charge Q) at xo distance from its center? (Consider that the surface of the
plate lies in the yz plane)
Solution
A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q
There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring.
So for a ring whose charge is q. we recall that the electric field it produces at distance x0 is given by
E = (1/
2-2)
Since, the actual ring (whose charge is da) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as
2.
= (1/
We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain
E = (x0/
2.
Evaluating the integral will lead us to
Qxo
1
E=
4 TEGR? X0 (x3 + R²)/2
For the case where in Ris extremely bigger than x0. Without other substitutions, the equation above will reduce to
E = Q/
E0)
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