Question

Two charges $2\mu C$ and $1\mu C$ are placed at a distance of 10cm. The distance of third charge from one of the charges so that it does not experience any force is:

• A. 4.14cm from $2\mu C$
• B. 5.858 cm from $2\mu C$
• C. 3.52 cm from $2\mu C$
• D. 6.48 cm from $2\mu C$

Answer 1

The correct option is B 5.858 cm from $2\mu C$

$\text{Step 1}:$ [Refer image $1$]

Assume a charge $q$ is placed at a distance $x$ from $2\mu C$

We have assumed that the charge $q$ is placed in between the region of $q_1$ and $q_2$. If it is not placed in this region then the net force on the charge $q$ would never be zero.

$\text{Step 2: Net force on charge q}$

$F_1:$ Force experinced by charge $q$ due to $1\mu C$

$F_2:$ Force experinced by charge $q$ due to $2\mu C$

Net force on charge $q$ is zero

$\therefore$ $F_1-F_2=0$

$\Rightarrow \frac{1}{4\pi ϵo}\frac{1\mu C\times q}{(10-x{)}^2}=\frac{1}{4\pi ϵo}\frac{2\mu C\times q}{x^2}$

$\Rightarrow \frac{1}{(10-x{)}^2}=\frac{2}{x^2}$

$\Rightarrow \frac{1}{10-x}=\frac{\sqrt{2}}{x}$

$\Rightarrow x=10\sqrt{2}-\sqrt{2}x$

$\Rightarrow x=\frac{10\sqrt{2}}{1+\sqrt{2}}$$=5.857cm$