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Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately:
Question

Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately:

A.

Parabolas

B.

Planes

C.

Ellipsoids

D.

Sphere

Correct option is D

The correct answer is (D) Sphere

Explanation:

When a collection of charges has a total non-zero charge, the equipotential surfaces at a great distance from the collection of charges are approximately spherical. This is because the electric field due to a point charge (or a collection of charges with a net charge) behaves as if it were a point source at a large distance, and the equipotential surfaces around such a charge are spherical in shape, radiating out symmetrically in all directions.
  • For a point charge, the electric field and the equipotential surfaces are spherical.

  • When the total charge is non-zero, the behavior of the field at large distances resembles that of a point charge, which leads to spherical equipotentials.

Information Booster:
  • Equipotential surfaces are surfaces where the electric potential is the same at every point on the surface.
  • The electric field is always perpendicular to the equipotential surfaces.

  • A spherical equipotential surface implies that the potential is uniform at any point on the surface, and the electric field radiates outward symmetrically.

  • At a great distance from a charge distribution, the electric field is weaker, and the system behaves like a point charge.

Additional Information:
  • Parabolas: Equipotentials around a uniform electric field are paraboloid in shape but are not relevant for point charges or charge distributions with a net charge.

  • Planes: Equipotential surfaces can be flat planes in the case of a uniform electric field, but this is not the case for distant regions from a collection of charges.

  • Ellipsoids: The electric field from a collection of charges with a dipole moment can produce ellipsoidal equipotential surfaces, but at great distances, this effect diminishes.

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