Question

Two electric charges q and -2q are placed at a distance 3a apart. The locus of points in the plane of the charges where the field potential is zero is:

• A. hyperbola
• B. straight line
• C. ellipse
• D. circle

Answer 1

Answer: (D)

Let at point (x, y) potential be zero.

then we have.

$\frac{kq}{\sqrt{x^2+y^2}}+\frac{k(-2q)}{\sqrt{(3a-x{)}^2+y^2}}=0$

$\frac{1}{\sqrt{x^2+y^2}}=\frac{2}{\sqrt{(3a-x{)}^2+y^2}}$

$(3a-x{)}^2+y^2=4x^2+4y^2$

$9a^2+x^2-6ax+y^2=4x^2+4y^2$

$\Rightarrow 3x^2+3y^2+6ax-9a^2=0$

$\Rightarrow y^2+(x+a{)}^2=4a^2$

$\therefore$ circle at center (-a, 0) with radius 2a.