 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-1/37c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

F^{μν} = \frac{1}{2} ϵ^{μν ρ σ} F_{ρ σ} .

(-, +, +, +)

and

ϵ^{0123} = + 1

F_{μν} F^{μν} = 2 (B^{2} - \frac{E ^{2}}{c ^{2}})

and

F_{μν} F^{μν} = - \frac{4}{c} E \cdot B .

F

can change the displayed overall signs but not their vanishing.

k

k \cdot E = 0, B = \frac{k \times E}{ω}, ω = c ∣ k ∣.

Hence

E \cdot B = 0, B^{2} = \frac{E ^{2}}{c ^{2}},

 New to topics? Read the docs here!