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COMEDK2024PhysicsCapacitance

A 5.80 ~F parallel plate air capacitor has a plate separation of 5 mm and is charged to a potential difference of 400 V . The energy density in the region between the plates is

Options

  1. A283 10⁻² ~J / m ^3
  2. B2.83 ~J / m ^3
  3. C2.83 10⁻⁴ ~J / m ^3
  4. D283 10^6 ~J / m ^3

Correct answer

C. 2.83 10⁻⁴ ~J / m ^3

Step-by-step solution

The energy density in the region between the plates is given by aligned u & = 1 2 ₀ E^2 & = 1 2 ₀ ( V d )^2 ( E= V d ) u & = 1 2 8.85 10⁻¹² ( 400 5 10⁻³ )^2 & =283.2 10⁻¹² 10^6 & =283.2 10⁻⁶ & =2.83 10⁻⁴ ~J / m ^3 aligned

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