Question

Find the distance of the point from $A$ where the net electric field will be zero for the given configuration.

• A. $0.4\text{m}$ towards left
• B. $1.4\text{m}$ towards left
• C. $2.4\text{m}$ towards left
• D. $3.4\text{m}$ towards left

Answer 1

The correct option is B $1.4\text{m}$ towards left

For the unlike charges, the net electric field is zero near smaller charge.
Let us say that the electric field is zero at a distance $x$ from A to the left.

The electric field due to $5\text{C}$ charge is $\frac{5k}{x^2}$ towards left.

The electric field due to $-100\text{C}$ charge is $\frac{100k}{(x+5{)}^2}$ towards right.

For the net electric field to be zero these two terms must be equal.

$\frac{5k}{x^2}=\frac{100k}{(x+5{)}^2}$

Simplifying this we get,

$\Rightarrow x=\frac{5}{\sqrt{\frac{100}{5}}-1}$

$\Rightarrow x=1.4\text{m}$ [from $A$ towards left]