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Electrostatics question

2008 · Shift 2 · Q56
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Electrostatics question

2008 · Shift 2 · Q56

JEE AdvancedPhysicsElectrostaticsMCQ+3 / −1
STATEMENT 1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits. and STATEMENT 2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by Q4πε0R{Q \over {4\pi {\varepsilon _0}R}}4πε0​RQ​
  1. A
    Statement 1 is True, Statement 2 is True; Statement 2 is a CORRECT explanation for Statement 1
  2. B
    Statement 1 is True, Statement 2 is True; Statement 2 is a NOT CORRECT explanation for Statement 1
  3. C
    Statement 1 is True, Statement 2 is False
  4. D
    Statement 1 is False, Statement 2 is True
View written solutionFree

Correct answer: B

  1. Analyze Statement 1

    Statement 1 says: For practical purposes, the earth is used as a reference at zero potential in electrical circuits.

    This is True.

    • The earth is a very large conductor.
    • Because of its enormous size, it can accept or supply charge without appreciable change in its potential.
    • Hence, in practice, it is taken as the reference point of zero potential.
  2. Analyze Statement 2

    Statement 2 says: The electrical potential of a sphere of radius RRR with charge QQQ uniformly distributed on the surface is given by V=Q4πε0RV=\frac{Q}{4\pi \varepsilon_0 R}V=4πε0​RQ​

    This is also True.

    For a charged spherical shell (or conducting sphere), the potential at the surface is V=14πε0QRV=\frac{1}{4\pi\varepsilon_0}\frac{Q}{R}V=4πε0​1​RQ​

    So Statement 2 is correct.

  3. Check whether Statement 2 explains Statement 1

    Statement 1 is about why the earth can be taken as zero potential reference.

    The relevant idea is that for a spherical conductor, V=14πε0QRV=\frac{1}{4\pi\varepsilon_0}\frac{Q}{R}V=4πε0​1​RQ​ and since the earth has a very large radius RRR, even if it gains or loses some charge, its potential changes only negligibly.

    However, Statement 2 merely gives the formula for the potential of a charged sphere. By itself, it does not explicitly explain the practical grounding idea unless we additionally apply it to the earth’s enormous radius.

    In assertion-reason type questions, the explanation must directly justify Statement 1. Here Statement 2 is true, but it is not the correct explanation as stated.

  4. Evaluate the options

    • A: Both true, and 2 explains 1 → Incorrect
    • B: Both true, but 2 does not explain 1 → Correct
    • C: 1 true, 2 false → Incorrect
    • D: 1 false, 2 true → Incorrect

Final Answer

Option B is correct.

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