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NCERT Exemplar · Q2

Q.A positive point charge +q+q is brought near an isolated (uncharged) conducting sphere. Four candidate electric-field-line patterns are proposed for this situation. In one pattern the field lines leave +q+q, reach the near side of the sphere and continue from its far side, and everywhere they touch the sphere they meet its surface at right angles (perpendicular), with a pattern symmetric about the line joining the charge and the sphere's centre. In a second pattern the lines on the far side of the sphere bend back and point toward the sphere and do not meet the surface perpendicularly. In a third pattern the lines continue past the sphere pointing outward but strike the sphere's surface obliquely rather than at right angles. In a fourth pattern the field lines on the far side of the sphere point inward, toward the sphere (arrows reversed). Which pattern correctly represents the electric field?

(a) The pattern in which the lines meet the conductor's surface perpendicularly everywhere and continue symmetrically past it.
(b) The pattern in which the far-side lines bend back toward the sphere and are not perpendicular to its surface.
(c) The pattern in which the lines strike the sphere's surface obliquely (not at right angles).
(d) The pattern in which the far-side field lines point inward, toward the sphere.
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✓ Free question

A conductor in electrostatic equilibrium can have no tangential electric field on its surface, so field lines must meet a conductor's surface at right angles. Only the first pattern shows this, with lines terminating on the induced negative charge (near side) and emerging from the induced positive charge (far side). That makes option (a) correct.

Concept

Electrostatic boundary condition at a conductor: the surface is an equipotential, so the field is normal (perpendicular) to the surface everywhere; any tangential component would move the free charges until it vanished.

Induced charges

The positive point charge induces negative charge on the near face of the (neutral) sphere and positive charge on the far face. Field lines from +q+q terminate on the near face; new lines emerge from the far face and run to infinity.

Applying it

  1. Demand E⃗⊥\vec{E}\perp surface at every point of the sphere.
  2. Only the first pattern (option a) shows the lines striking and leaving the sphere perpendicularly and in a symmetric way consistent with the induced-charge distribution.
  3. The other patterns violate either the perpendicularity rule or the required arrow directions.

Why the others fail

(b) Field lines on the far side bending back toward the sphere is unphysical and they are not normal to the surface. (c) Lines meeting the surface obliquely violate the conductor boundary condition. (d) Reversed (inward) arrows on the far side contradict the induced positive charge there.

✓Final answer

Option (a): the pattern in which the field lines meet the conductor's surface perpendicularly everywhere.

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