Question

In terms of basic units of mass $(M)$, length $(L)$, time $(T)$ and charge $(Q)$, the dimensions of magnetic permeability of vacuum $(\mu_0)$ would be

• A. $\left[ ML Q ^{-2}\right]$
• B. $\left[ L T^{-1} Q ^{-1}\right]$
• C. $\left[ ML ^{2} T ^{-1} Q ^{-2}\right]$
• D. $\left[ L TQ ^{-1}\right]$

Answer 1

Answer: (A)

$\left[ ML Q ^{-2}\right]$

Answer 2

The force per unit length experienced due to two wires in which current is flowing in the same direction is given by $\frac{d F}{d l} =\frac{\mu_{0}}{4 \pi} \frac{2 I_{1} I_{2}}{d}$ $\Rightarrow \frac{\left[ ML T ^{-2}\right]}{[ L ]} =\left[\mu_{0}\right] \frac{\left[ A ^{2}\right]}{[ L ]}$ $\Rightarrow \frac{\left[ MLT ^{-2}\right]}{[ L ]} =\mu_{0}\left[\frac{ O ^{2}}{ T ^{2} L }\right]$ $\Rightarrow \mu_{0} =\left[ ML Q ^{-2}\right]$