Question

If \(A\), \(B\) and \(C\) represent work done, distance and electric charge respectively, then the physical quantity having the dimensions of \[ \frac{C^2}{AB} \] is

• A. Permittivity
• B. Permeability
• C. Electric potential
• D. Electric energy

Hint:

Remember the standard dimensions: \[ [\varepsilon_0] = M^{-1}L^{-3}T^{4}I^{2}, \qquad [\mu_0] = MLT^{-2}I^{-2}. \] Questions on dimensions are often solved quickly by matching these standard forms.

Answer 1

The Correct Option is A

Concept: Dimensional analysis. A = work = \(ML^2T^{-2}\), B = distance = \(L\), C = charge = \(IT\). Find dimensions of \(C^2/(AB)\).

Step 1: \([C^2] = I^2T^2\). \([AB] = (ML^2T^{-2})(L) = ML^3T^{-2}\). \([C^2/(AB)] = M^{-1}L^{-3}T^4I^2\).

Step 2: Permittivity \(\varepsilon_0\) from Coulomb's law: \([\varepsilon_0] = \frac{Q^2}{F r^2} = \frac{I^2T^2}{(MLT^{-2})L^2} = M^{-1}L^{-3}T^4I^2\). Matches.

Step 3: Write the final answer. \(\boxed{\text{Permittivity}}\)