Question

A $3\mu C$ point charge is kept in an external uniform electric field of $1.6x{10}^{4}N{C}^{-1}$at what distance from the point charge the net electric field would be zero?

• A. $3m$
• B. $1.3m$
• C. $2m$
• D. $4.6m$

Answer 1

The correct option is B

$1.3m$

Step 1:Given data

$q=3\times {10}^{-6}C$

$E_1=1.6\times {10}^{4}N{C}^{-1}$

Step 2 : Formula used

The electric field due to charge $q$ is given by
$E=\frac{k\left|q\right|}{r^2}$
The distance when the electric field is zero is given by
$E_1=E_2$
$E_1=\frac{kq}{r^2}$

Step 3:Substitute the known values

$E_1=\frac{kq}{r^2}$

where $k$ is the constant value $9.0\times {10}^{9}N{m}^2{C}^{-2}iscoulombscons\tan t$

$16000=\frac{\left(9.0\times {10}^9\right)\left(3\times {10}^{-6}\right)}{r^2}$

$r^2=\frac{27000}{16000}$

$r^2=1.6875$

$$\begin{gathered} r=\sqrt{1.6875} \\ r=1.3m \end{gathered}$$

Hence, Option $B$ is the correct answer.

The distance from the point charge is $r=1.3m$. Therefore, the option $B$is the correct answer.