A physical quantity is given by X = B^2 ₀ , where B is the magnetic field and ₀ is the permeability of free space. If the dimensional formula of X is represented as M^a L^b T^c , then the value of a + b - c is

Step-by-step solution

The quantity X = B^2 ₀ is proportional to the energy density of a magnetic field. Energy density is defined as energy per unit volume. The dimensional formula of energy is [M L^2 T⁻²] . The dimensional formula of volume is [L^3] . Therefore, the dimensional formula of energy density is [M L^2 T⁻²] [L^3] = [M L⁻¹ T⁻²] . Comparing this with M^a L^b T^c , we get: a = 1 b = -1 c = -2 The value of a + b - c = 1 + (-1) - (-2) = 1 - 1 + 2 = 2 . Answer: 2