The electric flux is \(ϕ=\alpha \sigma +\beta \lambda\) where \(\lambda\) and \(\sigma\) are linear and surface charge d…

The electric flux \(\phi\) has dimensions of charge per unit area, i.e.,:

\([ϕ]=\left[\frac{Q}{\text{ Area }}\right]\)

a is associated with surface charge density s , which has the dimensions:

\([\sigma ]=\frac{Q}{\text{ Area }}\)

Thus, the dimensions of a will be:

\([\alpha ]=\left[\frac{ϕ}{\sigma }\right]=\frac{Q/\text{ Area }}{Q/\text{ Area }}=1\)

Next, for 1 , the linear charge density, we have:

\([\lambda ]=\frac{Q}{\text{ Length }}\)

Since b is associated with 1 , the dimensions of b are:

\([\beta ]=\left[\frac{ϕ}{\lambda }\right]=\frac{Q/\text{ Area }}{Q/\text{ Length }}=\frac{\text{ Length }}{\text{ Area }}\)

Now, considering the ratio \(\frac{\alpha }{\beta }\), we find:

\(\left[\frac{\alpha }{\beta }\right]=\frac{1}{\frac{\text{ Length }}{\text{ Area }}}=\text{ Length }\)

Thus, the ratio \(\frac{\alpha }{\beta }\) represents length.