A physical quantity is defined as P = ₀ E^2 c , where E is the electric field, ₀ is the permittivity of free space, and c is the speed of light in vacuum. If the dimensional formula of P is given by M^a L^b T^c , then the value of a^2 + b^2 + c^2 is

Step-by-step solution

The quantity ₀ E^2 is proportional to the energy density of an electric field. The dimensional formula of energy density (energy per unit volume) is [M L^2 T⁻²] [L^3] = [M L⁻¹ T⁻²] . The quantity c represents the speed of light, which has the dimensional formula [L T⁻¹] . Therefore, the dimensional formula of P = ₀ E^2 c is given by: [P] = [M L⁻¹ T⁻²] [L T⁻¹] = [M L^0 T⁻³] . Comparing this with M^a L^b T^c , we get: a = 1 b = 0 c = -3 The value of a^2 + b^2 + c^2 = (1)^2 + (0)^2 + (-3)^2 = 1 + 0 + 9 = 10 . Answer: