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Derive electric field due to an …

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Derive electric field due to an infinitely long straight uniformily charged wire
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Gaurav Seth 6 years, 11 months ago

Consider a thin infinitely long straight charged wire of linear charge density λ.

Let P be the point at a distance ‘a’ from the line. To find electric field at point P, draw a cylindrical surface of radius ‘a’ and length l.

If E is the magnitude of electric field at point P, then electric flux through the Gaussian surface is given by,

<dl> <dd>

Φ = E × Area of the curved surface of a cylinder of radius r and length l

Because electric lines of force are parallel to end faces (circular caps) of the cylinder, there is no component of field along the normal to the end faces.

</dd> </dl>

Φ = E × 2πal … (i)

According to Gauss theorem, we have

From equations (i) and (ii), we obtain

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