Question

The term ɛ₀E² (ɛ₀ = permittivity, E = electric field) is dimensionally incompatible with the term

(1) p (p = pressure)

(2) k/x (k = spring constant, x = displacement)

(3) CV² (C = capacitance, V = potential difference)

(4) (mgh/v) (m = mass, h = height, V = volume, g = acceleration due to gravity)

Answer 1

(3) CV² (C = capacitance, V = potential difference)

The term ɛ₀E² has the dimensions of energy density, i.e. energy per unit volume. [We know that the energy density, of the electric field, is 1/2 ɛ₀E² . (The dimensions of the term can also be obtained through a substitution of the dimensions of ɛ₀ and E)].

These terms are thus dimensionally compatible with the term ɛ₀E² .

This term is, therefore, dimensionally incompatible with ɛ₀E² .