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Electrostatics question

2007 · Shift 1 · Q49
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Electrostatics question

2007 · Shift 1 · Q49

JEE AdvancedPhysicsElectrostaticsMCQ+3 / −1
Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,
  1. A
    negative and distributed uniformly over the surface of the sphere
  2. B
    negative and appears only at the point on the sphere closest to the point charge
  3. C
    negative and distributed non-uniformly over the entire surface of the sphere
  4. D
    zero
View written solutionFree

Correct answer: D

Step-by-step Solution:

  1. Initial State of the Sphere: The problem states that we have a neutral conducting sphere. By definition, a neutral object has a net charge of zero. This means it contains an equal amount of positive and negative charge (protons and free electrons).

  2. Introducing an External Charge: A positive point charge is placed outside the sphere. This external charge will create an electric field in its vicinity.

  3. Electrostatic Induction: The electric field from the positive point charge exerts a force on the charges within the conducting sphere.

    • The free electrons (negative charges) in the conductor are mobile and will be attracted towards the external positive charge. They will accumulate on the surface of thesphere closer to the point charge.
    • The positive atomic nuclei are fixed in the metallic lattice, but their repulsion from the external positive charge results in a net positive charge on the side of the sphere farther away, as this region becomes deficient in electrons.
    • This separation of charges within a neutral conductor due to an external charge is called electrostatic induction.

  4. Calculating the Net Charge: The question asks for the net charge on the sphere after the point charge is brought near. The process of induction only causes a redistribution of the existing charges within the sphere. No charge is transferred to or from the sphere because it is electrically isolated. Therefore, the total number of positive charges and negative charges in the sphere remains the same. The algebraic sum of all charges on the sphere is still zero.

  5. Evaluating the Options:

    • A: negative and distributed uniformly over the surface of the sphere. Incorrect. The net charge is zero. Also, the induced charge distribution is non-uniform due to the proximity of the point charge.
    • B: negative and appears only at the point on the sphere closest to the point charge. Incorrect. The net charge is zero. The induced charge is distributed over a region, not a single point.
    • C: negative and distributed non-uniformly over the entire surface of the sphere. Incorrect. The net charge is zero, not negative.
    • D: zero. Correct. Since the sphere was initially neutral and no charge was added or removed, its net charge remains zero. The external charge only causes a separation of the existing positive and negative charges.
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