Consider the dimensional relation in which H equals x raised to power p, multiplied by ε raised to power q, multiplied by E raised to power r, and divided by t raised to power s. Here ε is permittivity, E is electric field, x is distance and t is time. The source paper states H as magnetic field, but its own note says the listed answer is obtained only when H is interpreted as magnetic-field intensity. Under that intended interpretation, what are p, q, r and s, respectively?
Options

Question

Consider the dimensional relation in which H equals x raised to power p, multiplied by ε raised to power q, multiplied by E raised to power r, and divided by t raised to power s. Here ε is permittivity, E is electric field, x is distance and t is time. The source paper states H as magnetic field, but its own note says the listed answer is obtained only when H is interpreted as magnetic-field intensity. Under that intended interpretation, what are p, q, r and s, respectively?

Options

G1 Physics · Accepted Answer

The source itself notes an ambiguity: if H is interpreted as magnetic flux density B, none of the listed options matches. Its marked answer is obtained by interpreting H as magnetic-field intensity. For magnetic-field intensity, [H] = A L⁻¹. The other dimensions are [x] = L, [E] = M L T⁻³ A⁻¹, [ε] = M⁻¹ L⁻³ T⁴ A², [t] = T. For the intended relation, H = (x raised to power p) × (ε raised to power q) × (E raised to power r) ÷ (t raised to power s). Equating dimensions gives A L⁻¹ = Lᵖ × (M⁻¹ L⁻³…