Question

Find the dimensions of

(a) electri field E,

(b) magnetic field B and

(c) magnetic permeability ${\mu }_0$.

The relevant equations are

$F=qE,F=qvB,$ and $B=\frac{{\mu }_{0}I}{2\pi a}$

where F is force, q is charge, v is speed, I is current, and a is distance.

Answer 1

(a) Electric field, $E=\frac{f}{q}$

$=\frac{\left[ML{T}^{-2}\right]}{\left[IT\right]}$

$=\left[ML{T}^{-3}{I}^{-1}\right]$

(b) Magnetic field, $B=\frac{F}{qv}$

$=\frac{\left[ML{T}^{-2}\right]}{\left[IT\right]\left[L{T}^{-}1\right]}=\left[M{T}^{-2}{I}^{-1}\right]$

(c) Magnetic permeability,

${\mu }_0=\frac{B\times 2\pi \alpha }{I}$

$=\frac{\left[M{T}^{-2}{I}^{-1}\right]\times \left[L\right]}{\left[I\right]}=\left[ML{T}^{-2}{I}^{-2}\right]$