The dimension of √μ₀/ϵ₀ is equal to that of: (μ₀ = Vacuum permeability and ϵ₀ = Vacuum permittivity)
❓ Question The dimension of μ 0 ε 0 is equal to that of: Options: Velocity Charge Magnetic field Current (Given: μ 0 \mu_0 = vacuum permeability, ε 0 \varepsilon_0 = vacuum permittivity.) 🖼️ Question Image ✍️ Short Solution Let’s analyze the dimensions of μ 0 ε 0 . Step 1 — Recall known relations in electromagnetism From Maxwell’s equations, the speed of light c c c in vacuum is related to μ 0 \mu_0 μ 0 and ε 0 \varepsilon_0 ε 0 as: c = 1 μ 0 ε 0 . c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}. 1 . Now take the reciprocal and modify it: μ 0 ε 0 = 1 ε 0 c . \sqrt{\frac{\mu_0}{\varepsilon_0}} = \frac{1}{\varepsilon_0 c}. But let’s instead focus on the dimensional relation . We know that: μ 0 ε 0 = 1 c . So, μ 0 ε 0 = μ 0 μ 0 ε 0 = μ 0 c . Thus, the dimension of μ 0 ε 0 = (dimension of μ₀) × (dimension of velocity) . Step 2 — Dimensional formula of μ₀ From the definition of magnetic field B B : B = μ 0 I 2 π r ...