Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field due to a Current
Using the formulae F = q v B and B = ₀ i 2 r , determine the SI units of the magnetic field B and the permeability constant ₀ respectively.
Options
- AN A ⁻¹ m and N m A ⁻²
- BN A ⁻¹ m ⁻¹ and N A ⁻²
- CN m A ⁻¹ and N A ⁻²
- DN A ⁻² m ⁻¹ and N A ⁻¹
Correct answer
B. N A ⁻¹ m ⁻¹ and N A ⁻²
Step-by-step solution
From the formula F = q v B , the magnitude of the magnetic field is given by B = F qv . Substituting the SI units, the unit of B is N C m s ⁻¹ . Since C s ⁻¹ = A , the unit of B is N A ⁻¹ m ⁻¹ . From the formula B = ₀ i 2 r , the permeability constant is given by ₀ = 2 r B i . Substituting the SI units, the unit of ₀ is m N A ⁻¹ m ⁻¹ A = N A ⁻² .