Let and denote small fractional changes in the permeability and permittivity of free space

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics

Problem

Let Δμ/μΔμ/μ and Δε/εΔε/ε denote small fractional changes in the permeability and permittivity of free space, respectively. Which relation correctly gives the corresponding fractional change Δc/cΔc/c in the speed of light? (a) Δc/c=−(Δμ/μ+Δε/ε)\displaystyle \Delta c/c = -\bigl(\Delta \mu/\mu + \Delta \varepsilon/\varepsilon\bigr) (b) Δc/c=Δμ/μ+Δε/ε2\displaystyle \Delta c/c = \dfrac{\Delta \mu/\mu + \Delta \varepsilon/\varepsilon}{2} (c) Δc/c=−Δμ/μ+Δε/ε2\displaystyle \Delta c/c = -\dfrac{\Delta \mu/\mu + \Delta \varepsilon/\varepsilon}{2} (d) Δc/c=−Δμ/μ−Δε/ε2\displaystyle \Delta c/c = -\dfrac{\Delta \mu/\mu - \Delta \varepsilon/\varepsilon}{2}

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