Question

$1\mu \text{C}$ charge is uniformly distributed on a spherical shell given by equation $x^2+y^2+z^2=25$. The intensity of electric field at a point $P(1,1,2)\text{m}$ is .

Answer 1

Given:
Equation of spherical shell,$x^2+y^2+z^2=25$
$\Rightarrow x^2+y^2+z^2=5^2$
On comparing it with equation of sphere,$x^2+y^2+z^2=r^2$, we get radius, $r=5\text{m}$.

Also,$OP=\sqrt{(x_2-x_1{)}^2(y_2-y_1{)}^2+(z_2-z_1)}$
$OP=\sqrt{(1-0{)}^2(1-0{)}^2+(2-0)}$
$OP=\sqrt{6}=2.45\text{m}<\text{5 m}$

Therefore point $P$ lies inside the spherical shell.
We know that for any uniformly charged spherical shell, electric field at any point inside the shell is zero.