Question

Two fixed charges $-2Q$ and $+Q$ are located at points $(-3a,0)$ and $(+3a,0)$ respectively, Then which of the following statement is correct?

• A. Points where the electric potential due to the two charges is zero in the x-y plane, lie on a circle of radius $4a$ and centre $(5a,0)$
• B. Potential is zero at $x=a$ and $x=9a$
• C. Both (a) and (b) are wrong
• D. Both (a) and (b) are correct

Answer 1

Answer: (D)

Both (a) and (b) are correct

Here, $V(x,y)=k[\frac{(-2Q)}{\sqrt{(x+3a{)}^2+y^2}}+\frac{Q}{\sqrt{(x-3a{)}^2+y^2}}]$

If $V(x,y)=0$ , then $\frac{4}{(x+3a{)}^2+y^2}=\frac{1}{(x-3a{)}^2+y^2}$

or $4x^2-24xa+36a^2+4y^2=x^2+6ax+9a^2+y^2$

or $3x^2-30xa+27a^2+3y^2=0$

or $x^2-10xa+9a^2+y^2=0$

or $x^2-2.x.5a+(5a{)}^2-(5a{)}^2+9a^2+y^2=0$

or $(x-5a{)}^2+y^2=16a^2=(4a{)}^2...\left(1\right)$

This is a equation circle of radius 4a and center $(5a,0)$

for zero potential along x axis , put $y=0$ in (1), we get

$(x-5a){=}_{-}^{+}4a$ or $x=+4a+5a=9aor-4a+5a=a$