Question

A charge of magnitude $Q$ is placed at the origin. A second identical charge is placed at the position $x=d$ along the x-axis. Other than infinitely far away, at what position on the x-axis will a positive test charge experience a zero net force?

• A. $x=-d$
• B. $x=-\frac{d}{2}$
• C. $x=\frac{d}{2}$
• D. $x=-\frac{3d}{2}$
• E. Cannot be determined from the given information

Answer 1

The correct option is C $x=\frac{d}{2}$

Let the electric field $E$ is zero at a point $P$ between the two given charges , at a distance $x$ from the charge $Q$ which is at the origin .

at point $P$, electric field due to $Q$ at origin

$E_1=\frac{KQ}{x^2}$

at point $P$, electric field due to $Q$ at a distance $d$ from $Q$ at origin

$E_2=\frac{KQ}{(d-x{)}^2}$

as $E_1$ and $E_2$ are in opposite direction due to two positive charges and electric field is zero at point $P$ , therefore

$E_1=E_2$

or $\frac{KQ}{x^2}=\frac{KQ}{(d-x{)}^2}$

or $x^2=(d-x{)}^2$

or $x=\frac{d}{2}$ or $\frac{3d}{2}$

but $x=\frac{3d}{2}$ is not possible as point $P$ is in between the two charges .

now if we put a positive test charge q at point $P$ , force on it

$F=qE=q\times 0=0$

option C is correct .