Question

A spherical volume contains a uniformly distributed charge density of $2\times {10}^{-4}C{m}^{-3}$. The electric field at a distance of $4cm$ from the centre is :

• A. $3\times {10}^5$
• B. $3\times {10}^4$
• C. $2\times {10}^5$
• D. $3\times {10}^6$

Answer 1

The correct option is A $3\times {10}^5$

Given data :

Electrical charge density, $\rho =2\times {10}^{-4}\frac{C}{m^{-3}}$

Radius of Gaussian sphere, $r=4cm=4\times {10}^{-2}m$

We know, electrical charge density is given by:

$\rho =\frac{q}{v}$ ......................(1)

where, $q$ is charge on sphere and $V$ is volume of sphere given as:

$V=\frac{4}{3}\pi r^3$

$V=1.33\times 3.14\times (4\times {10}^{-2}{)}^3$

$V=26.72\times {10}^{-5}{m}^3$ ..................(2)

Therefore, from (1)

$q=\rho V$

$q=2\times {10}^{-4}\times 26.72\times {10}^{-5}$

$q=53.44\times {10}^{-9}C$ .....................(3)

Now, the electric field is:

$E=\frac{kq}{r^2}$

$E=\frac{8.99\times {10}^9\times 53.44\times {10}^{-9}}{(4\times {10}^{-2}{)}^2}$

$E=\frac{480.42}{16\times {10}^{-4}}$

$E=30\times {10}^4$

$E=3\times {10}^5\frac{N}{C}$