Question

1) A spherical conductor of radius $12cm$ has a charge of $1.6\times {10}^{-7}C$ distributed uniformly on its surface. What is the electric field?
A) Inside the sphere

2) A spherical conductor of radius $12cm$ has a charge of $1.6\times {10}^{-7}C$ distributed uniformly on its surface. What is the electric field?
B) Just outside the sphere


3) A spherical conductor of radius $12cm$ has a charge of $1.6\times {10}^{-7}C$ distributed uniformly on its surface. What is the electric field?
C) At a point $18cm$ from the centre of the sphere?

Answer 1

1) From Gauss Law:

$\oint \overrightarrow{E.}\overrightarrow{dA}=\frac{q_{in}}{{ϵ}_o}$


As $E$ is constant in magnitude at any $r$ in all direction and angle between $\overrightarrow{E}$ and $\overrightarrow{A}$ is $0^{\circ }$

$E\oint dA=\frac{q_{in}}{{ϵ}_0}$

$E.4\pi r^2=\frac{q_{in}}{{ϵ}_0}$

$E=\frac{q_{in}}{4\pi {ϵ}_0{r}^2}E=\frac{K{q}_{in}}{r^2}$ ...(i)

As $r<R$

$q_{in}=0$

$E=0$

2) From Gauss Law:

$\oint \overrightarrow{E.}\overrightarrow{dA}=\frac{q_{in}}{{ϵ}_o}$

As $E$ is constant in magnitude at any $r$ in all direction and angle between $\overrightarrow{E}$ and $\overrightarrow{A}$ is $0^{\circ }$

$E\oint dA=\frac{q_{in}}{{ϵ}_0}$

$E.4\pi r^2=\frac{q_{in}}{{ϵ}_0}$

$E=\frac{q_{in}}{4\pi {ϵ}_0{r}^2}E=\frac{K{q}_{in}}{r^2}$ ...(i)

$q_{in}=1.6\times {10}^{-7}C$

$R=12cm=0.12m$

$E=\frac{9\times {10}^9\times 1.6\times {10}^{-7}}{(0.12{)}^2}$

$E={10}^{5}N/C$

3) From Gauss Law:

$\oint \overrightarrow{E.}\overrightarrow{dA}=\frac{q_{in}}{{ϵ}_o}$

As $E$ is constant in magnitude at any $r$ in all direction and angle between $\overrightarrow{E}$ and $\overrightarrow{A}$ is $0^{\circ }$

$E\oint dA=\frac{q_{in}}{{ϵ}_0}$

$E.4\pi r^2=\frac{q_{in}}{{ϵ}_0}$

$E=\frac{q_{in}}{4\pi {ϵ}_0{r}^2}E=\frac{K{q}_{in}}{r^2}$ ...(i)

$q_{in}=1.6\times {10}^{-7}C$

$r=0.18m$

$E=\frac{9\times {10}^9\times 1.6\times {10}^{-7}}{(0.18{)}^2}$

$=4.4\times {10}^{4}N/C$