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ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2022/paper-1/section-c/c8/b/solution

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Past exam of the physics B course of the University of Cambridge / 2022 / Paper 1 / Section C / C8 / b / Solution by

Codex  0 2026-10-18

The unit relative permittivity and vacuum-valued magnetic permeability imply

D = ϵ_{0} E

and

B = μ_{0} H

. The electromagnetic energy per unit volume is

U = \frac{1}{2} ϵ_{0} E \cdot E + \frac{1}{2} μ_{0} H \cdot H, [U] = J m^{- 3} .

The two contributions are the stored electric and magnetic energies. Although called

U

in this paper, this quantity is an energy density; the total electromagnetic energy is

\int_{V} U d V

.

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