Determine the dimensions of the magnetic permeability ₀ . The relevant equations are F = qE , F = qvB , and B = ₀ I 2 a ; where F is force, q is charge, v is speed, I is current, and a is distance.

Step-by-step solution

From the given formula B = ₀ I 2 a , we get ₀ = 2 a B I . From the magnetic force formula F = qvB , we get B = F qv . Substituting the expression for B gives ₀ = 2 a F qvI . The dimensional formulas for the quantities are: [F] = MLT⁻² [a] = L [q] = IT [v] = LT⁻¹ [I] = I Substituting these dimensions into the expression for ₀ : [ ₀] = MLT⁻² L (IT)(LT⁻¹)I [ ₀] = ML^2T⁻² L I^2 [ ₀] = MLT⁻²I⁻²