Question

Using the formula \[\vec{F} = q \vec{v} \times \vec{B} \text{ and } B = \frac{\mu_0 i}{2\pi r}\]show that the SI units of the magnetic field B and the permeability constant µ₀ may be written as N mA⁻¹ and NA⁻² respectively.

Answer 1

Using the relation \[\vec{F} = q v^\rightharpoonup \times \vec{B}\] , we get

\[B = \frac{F}{qv}\]
\[ = \frac{F}{Itv}\]

Units of
Force (F) = N 
Current (I) = A
Time (T) = s
Velocity (v) = m/s

\[\Rightarrow B = N/A - m\]

Now, using the relation

\[B = \frac{\mu_0 i}{2\pi r}\]\[B = \frac{\mu_0 i}{2\pi r}\], we get

\[\Rightarrow \mu_0 = B\frac{2\pi r}{i} = \frac{N}{A - m} \times \frac{m}{A}\]

\[ \Rightarrow \mu_0 = N/ A^2\]