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Question

The electric field in a region is radially outwards with magnitude E=αR. Calculate the charge contained in a sphere of radius R centred at the origin. If the value of charge is m×1010 C, then find m. (Given α=100 V/m2 and R=0.30 m)

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Solution

We know that net electric flux can be given by
ϕnet=E.S

Since, the electric field is radially outwards, the angle between electric field and area vector will be 0
ϕnet=E.S.cos(0)
ϕnet=αR4πR2
ϕnet=α4πR3-----(i)

By Gauss law, we know that
ϕnet=Qinϵ0
By using (i), we can write
4παR3=Qinϵ0
Qin=4πϵ0αR3
Qin=19×109×100×(0.3)3

Qin=3×1010 C
m=3

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