Physical quantities of electric permittivity with dimensions

To answer the question, we need to understand the concept of electric permittivity and its dimensions. Electric permittivity is a physical quantity that measures the ability of a material to store electrical energy in an electric field. It is denoted by the symbol ε (epsilon) and is measured in units of farads per meter (F/m).

Step 1: Understand the concept of electric permittivity Electric permittivity is a property of a material that determines how it responds to an electric field. It quantifies the ability of the material to store electrical energy in the presence of an electric field.

Step 2: Determine the dimensions of electric permittivity To determine the dimensions of electric permittivity, we need to analyze its unit, which is farads per meter (F/m). The farad (F) is the unit of capacitance, and the meter (m) is the unit of length.

Step 3: Break down the dimensions The dimension of capacitance (C) is given by the equation C = Q/V, where Q represents charge and V represents voltage. The dimensions of charge (Q) are given by [Q] = [I] * [T], where [I] represents current and [T] represents time. The dimensions of voltage (V) are given by [V] = [E] * [L], where [E] represents energy and [L] represents length.

Step 4: Combine the dimensions Combining the dimensions, we have [C] = [I] * [T] / ([E] * [L]). Rearranging the equation, we get [E] = [I] * [T] / ([C] * [L]).

Step 5: Substitute the dimensions of electric permittivity Substituting the dimensions of electric permittivity, we have [ε] = [I] * [T] / ([C] * [L]).

Step 6: Simplify the equation Simplifying the equation, we have [ε] = [I] * [T] / ([C] * [L]) = [I] * [T] * [L] / [C].

Step 7: Finalize the dimensions Therefore, the dimensions of electric permittivity are given by [ε] = [I] * [T] * [L] / [C].

In conclusion, the dimensions of electric permittivity are given by [ε] = [I] * [T] * [L] / [C].