Which of the following statement is CORRECT regarding the locus of point on this plane where the potential has a value zero,if two electric charges q and -2q are placed at a distance 6m apart on a horizontal plane.

Question

Question

This question was previously asked in

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 1)

Answer 1

Concept:

The general equation of a circle is x² + y² + 2gx + 2fy + c = 0

Centre of circle = (-g , -f)

Radius of circle = √(g² + f² - c)

Formula:

Potential of a point charge = kq/r

Calculations:

Given: q1 = q, q2 = -2q

F2 Savita Engineering 28-6-22 D4

Let us take a general point (x , y) on the xy-plane.

Potential at this point = \(\frac{kq} {\sqrt {(x - 0)^2 + (y - 0)^2}} + \frac{-2kq} {\sqrt {(x - 6)^2 + (y - 0)^2}}\)

Putting it equal to zero for zero potential plane,

⇒ \(\frac{kq} {\sqrt {(x - 0)^2 + (y - 0)^2}} + \frac{-2kq} {\sqrt {(x - 6)^2 + (y - 0)^2}}\) = 0

⇒ (x - 6)2 + (y - 0)2 = 4[(x - 0)2 + (y - 0)2]

⇒ x2 + 36 - 12x + y2 = 4x2 + 4y2

⇒ 3x²+ 3y² + 12x - 36 = 0

⇒ x2 + y2 + 4x - 12 = 0

The above is representing a circle. Comparing with the equation of a circle :

Centre = (-2 , 0)

Radius = √[(-2)² + (0)² - (-12)] = 4 m

So, the correct answer is option 3.