A student determines a dimensionless quantity, B= en2ε0hc. Findd the value of n. (here, e = electric charge, ε0 electric permittivity of vacuum, h = Planck's constant and c = speed of light.)

Dimension of B = [M0L0T0]Dimension e = [AT]Dimensions ε0= [A2M-1L-3T4]Dimensions h = [ML2T-1]Dimension c = [LT-1]∴ [M0L0T0] = [AT]n[A2M-1L-3T-4][ML2T-1][LT-1]or [M0L0T0] = [An-2L0Tn-2]∴n -2 = 0⇒n = 2