Can gauss save us?

Electricity and Magnetism Level 4

The surface charge density \( \sigma \) of a non conducting disc of radius 'R' varies as \( \sigma = br \) , where b is a positive constant and r is the distance from the centre of the disc.

Find the electric field caused by the disc at a point along the axis of the disc and a distance x from its centre.

Details and assumptions :

Find the absolute value of electric field at distance in SI units.

\( R = x = 1 m \)

\( b = 10^{-9} \dfrac{C}{m^{3}} \)

\( \dfrac{1}{4 \pi \epsilon_{0}} = 9\times 10^{9} \dfrac{Nm^{2}}{C^{2}} \)

\( \epsilon_{0} \)is permittivity of free space.

Round off your answer to the nearest integer.

I Would advice not to use wolfram alpha for performing integration as it would be a nice exercise to evaluate that integral with hand


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