Home
Class 12
PHYSICS
Two point charges of magnitude +q and -q...

Two point charges of magnitude `+q and -q` are placed at `(-d//2,0,0) and (d//2,0,0)` are respectively. Find the equation of the euipotential surface where the potential is zero.

Text Solution

Verified by Experts

Fig shows two point charges `+q` at `A (-(d)/(2) ,0,0)` and charge `-q at B ((d)/(2),0,0)` with center at 0, Let the equipotential surface (with `V = 0`) be at a distance x from the origin 0.
The potential at any point P on the surface at a height h from AB is
`V = (q)/(4pi in_(0) [(x + d//2)^(2) + h^(2)]^(1//2)) - (q)/(4pi in_(0) [(x - d//2)^(2) + h^(2)]^(1//2))`
then `V = 0`, then `(q)/(4pi in_(0) [(x + d//2)^(2) + h^(2)]^(1//2)) = (q)/(4pi in_(0) [(x - d//2)^(2) + h^(2)]^(1//2))`
or `(x + d//2)^(2) + h^(2) = (x - d//2)^(2) + h^(2) or x^(2) + (d^(2))/(4) + xd = x^(2) + (d^(2))/(4) -xd or 2xd = 0 or x = 0`.
Hence `x = 0` is the epuation of the euipotential surface where potential is zero.
Promotional Banner

Similar Questions

Explore conceptually related problems

Two charges q_(1) and q_(2) are placed at (0,0,d) and (0,0,-d) respectively. Find locus of points where the potential is zero.

Two charges q_(1) and q_(2) are placed at (0,0d) and (0,0-d) respectively. Find locus of points where the potential is zero.

" Two point charges "+2q" and "-q" are placed on "x" -axis at "(0,0,0)" and "(3,0,0)" respectively,How many points of zero electric potential are there in the plane "X=5?

Two point charges +q and -q are held fixed at (-d,o) and (d,0) respectively of a x-y coordinate system. Then

Consider a spherical surface of radius 4 m cenred at the origin. Point charges +q and - 2q are fixed at points A( 2 m, 0,0) and B( 8 m, 0, 0), respectively. Show that every point on the shperical surface is at zero potential.

The point charges q_(1)=1 muC,q_(2)=-2 muC and q_(3)=3 muC are placed at (1m,0,0),(0,2m,0) and (0,0,3m) respectively. Find the electric potential at origin.

Three point charge q_1=1muC, q_2=-2muC and q_3=3muC are placed at (1m, 0,0), (0,2m,0) and (0,0,3m) respectively. Find the electric potential at as origin.