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Electric Fields

Electric potential energy and capacitance of a sphere

  • 3 things to know
  • Papers 1, 2 and 3

Overview

Recall questions on electric potential energy of a charge near a point charge with calculations, deriving and calculating the capacitance of an isolated sphere, and the area under a force-distance graph.

What you need to know

Answer each one before you reveal it.

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Numbers

State the capacitance of an isolated conducting sphere, and the two equations used to derive it.

Key term

What is the starting equation for deriving the capacitance of an isolated sphere?

Key term

Which definition of capacitance is used when deriving the capacitance of an isolated sphere?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the relationship between electric potential energy, charge, and electric potential.

    Model answer

    Electric potential energy equals the product of the charge and the electric potential: Eₚ = qV.

  2. 2

    Write the equation for the electric potential energy of a charge q at distance r from a point charge Q.

    Model answer

    Eₚ = Qq/(4πε₀r), where Eₚ is electric potential energy, Q and q are the charges, ε₀ is the permittivity of free space, and r is the separation.

  3. 3

    What quantities are needed to calculate the electric potential energy of a charge near a point charge?

    Model answer

    Both charges (Q and q), the separation between them (r), and the permittivity of free space (ε₀).

  4. 4

    Calculate the electric potential energy when charge Q = 4.0 × 10⁻⁹ C, charge q = 2.0 × 10⁻⁹ C, distance = 0.46 m.

    Model answer

    Electric potential energy = (4.0 × 10⁻⁹ × 2.0 × 10⁻⁹) ÷ (4π × 8.85 × 10⁻¹² × 0.46) = 1.56 × 10⁻⁷ J.

  5. 5

    State the equation for the capacitance of an isolated conducting sphere.

    Model answer

    C = 4πε₀R, where C is capacitance, ε₀ is the permittivity of free space, and R is the radius of the sphere.

  6. 6

    What is the starting equation for deriving the capacitance of an isolated sphere?

    Model answer

    V = Q/(4πε₀R), which gives the electric potential at the surface of the sphere.

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