MPSC 2026 Prelims Paper-I · Question 51 of 100

This question was CANCELLED by the Maharashtra Public Service Commission. This card therefore contains no analysis of a correct answer and nominates none — the Commission has struck the question out, and there is nothing to nominate. Two features of the printed page are worth a candidate's attention, because both are visible without any inside knowledge. The first is that the English stem does not say what kind of point charge it means. For an isolated point charge the equipotential surfaces are concentric spheres centred on the charge, and the electric field at any point on such a sphere is along the radius. But a positive charge produces a field pointing away from it and a negative charge a field pointing towards it. Both directions are printed on the page — 'Radial outward' at option (1) and 'Radial inward' at option (4) — and nothing in the stem tells the candidate which charge is in front of him. A question that offers both halves of a sign ambiguity and then omits the sign is asking the candidate to guess. The second is that the two remaining choices say the same thing twice. Option (2) is 'Parallel to the surface' and option (3) is 'Tangential', and for a smooth surface a tangential direction is a direction parallel to the surface at that point. They are one physical claim printed under two labels, and both fall to the same standard result — that the field must be perpendicular to an equipotential surface everywhere, which is set out in the background below. There is also a divergence between the two language columns of the booklet. The English asks for the direction of the electric field of a point charge at a point on its equipotential surface. The Marathi column reads 'विद्युत क्षेत्राच्या समतुल्य पृष्ठभागावरील कोणत्याही बिंदूवर त्याला विद्युत प्रभारित करण्यासाठी विद्युत क्षेत्राची दिशा काय असावी ?' — which speaks of the equipotential surface of an electric field, contains no equivalent of 'point charge', and adds a clause about charging the object that has no counterpart in the English. A candidate reading Marathi was not being handed the same question as one reading English. The physics below is worth learning regardless. The question was faulty; the topic is not, and it returns in every general science paper.

An equipotential surface is a surface every point of which is at the same electric potential. The single most useful consequence follows immediately from the definition of potential difference: the work done in moving a charge q between two points is W = q(V₁ − V₂), so moving a charge from one point of an equipotential surface to another does no work at all, because the potential difference is zero. Now, work is done only by the component of force along the displacement. If the electric field had any component lying along the surface, moving a charge in that direction would do work, and the two points could not be at the same potential. Therefore the electric field must have no component along an equipotential surface — it must be perpendicular, that is normal, to the surface at every point. This holds for every charge configuration whatever, not merely for a point charge, and it is the result from which the standard pictures follow. For an isolated point charge the potential is V = kq/r, so a surface of constant V is a sphere of constant r centred on the charge, and the normal to a sphere is the radial direction — hence a radial field. For a uniform field the equipotentials are parallel planes at right angles to the field lines. For an infinitely long straight line of charge they are coaxial cylinders. In each case the field lines and the equipotential surfaces cross at right angles.

Several further properties come out of the same reasoning and are examined as often as the perpendicularity result itself. Two equipotential surfaces can never intersect, because a point lying on both would have to have two different potentials at once. Equipotential surfaces are crowded together where the field is strong and spread apart where it is weak, since the field is the negative gradient of potential — a large change of potential over a small distance means a large field. The surface of any conductor in electrostatic equilibrium is an equipotential surface, and the whole body of the conductor is at that same potential, which is why the field just outside a charged conductor stands perpendicular to its surface; it is also why the field inside a conductor in equilibrium is zero and why charge resides on the outer surface. The practical applications a science paper likes to draw on are electrostatic shielding and the Faraday cage, the behaviour of a lightning conductor, and the design of high-voltage equipment with rounded surfaces to avoid the intense fields that gather at sharp points. In Maharashtra's higher secondary syllabus this material sits in the electrostatics chapter alongside Gauss's law and capacitance, and MPSC draws on it at exactly that level.

• An equipotential surface is one on which the potential is the same at every point. No work is done in moving a charge from one point of it to another, because the potential difference is zero.
• The electric field is always perpendicular to an equipotential surface. If it had a component along the surface, moving a charge in that direction would do work and the surface could not be equipotential. This holds for every charge distribution.
• For an isolated point charge the equipotential surfaces are concentric spheres centred on the charge, and the field along the normal to those spheres is radial — directed away from a positive charge and towards a negative one.
• For a uniform field the equipotential surfaces are parallel planes perpendicular to the field; for an infinite line charge they are coaxial cylinders. Two equipotential surfaces can never intersect, since a point of intersection would have two potentials.
• The surface of a conductor in electrostatic equilibrium is an equipotential surface and the field just outside it is normal to the surface; the field inside the conductor is zero and the excess charge resides on the outer surface — the basis of electrostatic shielding.

• Forgetting that the sign of the charge fixes the direction of a radial field. Outward for positive, inward for negative — the geometry is radial in both cases, and only the sign chooses between them.
• Believing the field is tangential to an equipotential surface. It is perpendicular; a tangential component would do work along the surface and destroy the equality of potential.
• Confusing zero potential with zero field, or zero field with zero potential. Each can occur without the other — the field is the gradient of the potential, not the potential itself.
• Assuming equipotential surfaces are always spheres. They are spheres only for a point charge or a spherically symmetric distribution; a uniform field gives planes and a line charge gives cylinders.

General science in MPSC Paper-I stays at higher secondary level and returns to electrostatics regularly. The reliable shapes are a definition question — what an equipotential surface is, or what its defining property implies; a geometry question — the shape of the equipotential surfaces for a given charge configuration; and a consequence question — why no work is done along such a surface, why two of them cannot intersect, or why the field is perpendicular at the surface of a conductor. All of these are answered from one idea, that the field is the negative gradient of potential, so a candidate who understands that relation rather than memorising the pictures can reconstruct every case. Note also that direction questions in this area are only well posed when the sign of the charge is given, which is a good reason to check that the stem has supplied it before committing an answer on a paper with negative marking.

No directly related past PYQ was found.

• practice — not a real PYQ

  Why is no work done in moving a charge from one point to another on an equipotential surface ?

  • (a)Because the electric field on the surface is zero
  • (b)Because the potential difference between the two points is zero
  • (c)Because the charge does not move through any distance
  • (d)Because the surface offers no resistance to motion

  Answer(b) Because the potential difference between the two points is zero. The work done in moving a charge q through a potential difference is W = qΔV, and on an equipotential surface ΔV is zero by definition, so W is zero however far the charge travels along it. The field on the surface is generally not zero — it is perpendicular to the surface, which is why it does no work on a displacement lying within the surface.

• practice — not a real PYQ

  For a uniform electric field, the equipotential surfaces are :

  • (a)concentric spheres
  • (b)coaxial cylinders
  • (c)parallel planes perpendicular to the field
  • (d)parallel planes along the direction of the field

  Answer(c) parallel planes perpendicular to the field. The field must be normal to every equipotential surface, so in a uniform field, where the field has the same direction everywhere, the surfaces are flat planes standing at right angles to it. Concentric spheres belong to a point charge and coaxial cylinders to an infinite line charge; planes lying along the field direction would make the field tangential to the surface, which is impossible.