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Electrostatics question

2022 · 29 Jul · Shift 1 · Q58
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  5. /2022 · 29 Jul · Shift 1 · Q58

Electrostatics question

2022 · 29 Jul · Shift 1 · Q58

JEE MainPhysicsElectrostaticsMCQ+4 / −1
Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options given below.
  1. A
    Both Statement I and Statement II are correct
  2. B
    Both Statement I and Statement II are incorrect
  3. C
    Statement I is correct but Statement II is incorrect
  4. D
    Statement I is incorrect but Statement II is correct
View written solutionFree

Correct answer: A

  1. Analyse Statement I: "Electric potential is constant within and at the surface of each conductor."

    For a conductor in electrostatic equilibrium:

    • The electric field inside the conductor is zero, i.e. E⃗=0\vec{E}=0E=0.
    • Since E⃗=−∇V,\vec{E} = -\nabla V,E=−∇V, if E⃗=0\vec{E}=0E=0, then the potential does not change from point to point inside the conductor.
    • Also, the entire surface of a conductor is an equipotential surface.

    Therefore, electric potential is constant throughout the conductor and on its surface.

    So, Statement I is correct.

  2. Analyse Statement II: "Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point."

    In electrostatic equilibrium:

    • If there were any tangential component of electric field on the conductor surface, free charges would move along the surface.
    • But in equilibrium, charges are at rest.
    • Hence, the tangential component of electric field must be zero.

    Therefore, the electric field just outside the conductor can only have a normal component, i.e. it must be perpendicular to the surface.

    So, Statement II is correct.

  3. Conclusion:

    • Statement I is correct.
    • Statement II is correct.

    Hence, the correct option is: A: Both Statement I and Statement II are correct\boxed{\text{A: Both Statement I and Statement II are correct}}A: Both Statement I and Statement II are correct​

  4. Comparison with stored answer:

    • Derived answer: A
    • Stored correct answer: A
    • They match.
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