Question

Two point charges $Q$ and $-Q/4$ are separated by a distance $x$ . Then

• A. potential is zero at a point on the axis which is $x$ / 3 on the right side of the charge $-Q/4$
• B. potential is zero at a point on the axis which is $x$ / 5 on the left side of the charge $-Q/4$
• C. electric field is zero at a point on the axis which is at a distance $x$ on the right side of the charge $-Q/4$
• D. there exist two points on the axis where electric field is zero.

Answer 1

Answer: (A), (B), (C)

The correct options are
A potential is zero at a point on the axis which is $x$ / 3 on the right side of the charge $-Q/4$
B potential is zero at a point on the axis which is $x$ / 5 on the left side of the charge $-Q/4$
C electric field is zero at a point on the axis which is at a distance $x$ on the right side of the charge $-Q/4$


$V_p=\frac{KQ}{x+r}-\frac{KQ/4}{r}=0$

$\Rightarrow \frac{1}{x+r}-\frac{1}{4r}=0$

$\Rightarrow 4r-x-r=0$

$r=\frac{x}{3}$

$V_p=\frac{-KQ/4}{r}+\frac{KQ}{(x-r)}=0$

$\Rightarrow -\frac{1}{4r}+\frac{1}{x-r}=0$

$\Rightarrow r=\frac{x}{5}$



$E_p=\frac{KQ}{(x+r{)}^2}-\frac{K\left(Q/4\right)}{r^2}=0$

and $r>0$
$⟹$ $x=r$