First slide

Electric field

Question

The electric field in a certain region is acting radially outward and is given by E = A r . A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by

Moderate

A

$4 π ε_{0} A a^{3}$
B

$ε_{0} A a^{3}$
C

$4 π ε_{0} A a^{2}$
D

$A ε_{0} a^{2}$

Solution

According to question, electric field varies as E =Ar
Here r is the radial distance.
At r = a, E = Aa . . . (i)
Net flux emitted from a spherical surface of radius a is
$ϕ_{net} = \frac{q_{e n}}{ε_{0}}$
$\Rightarrow (A a) \times (4 π a^{2}) = \frac{q}{ε_{0}} [Using equation (i) ]$
$∴ q = 4 π ε_{0} A a^{3}$

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