Determine the dimensions of the magnetic permeability μ_0 . The relevant equations are F = qE , F = qvB , and B = (μ_0 I)/(2 π a) ; where F is force, q is charge, v is speed, I is current, and a is distance.

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Correct answer: B. MLT^ -2 I^ -2

From the given formula B = (μ_0 I)/(2 π a) , we get μ_0 = (2 π a B)/(I) . From the magnetic force formula F = qvB , we get B = (F)/(qv) . Substituting the expression for B gives μ_0 = (2 π 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 μ_0 : [μ_0] = MLT^ -2 L (IT)(LT^ -1 )I [μ_0] = ML^2T^ -2 L I^2 [μ_0] = MLT^ -2 I^ -2

Determine the dimensions of the magnetic permeability μ_0 . The...

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