Question

Define the term 'electric flux' and write its dimensions.

Hint:

Electric flux represents the number of electric field lines passing through a surface. Its dimensions are derived from the electric field and area.

Answer 1

Step 1: Electric flux is defined as the product of the electric field and the area through which the field lines pass, and it is given by:
\[ \Phi_E = \vec{E} \cdot \vec{A} \] where \( \vec{E} \) is the electric field and \( \vec{A} \) is the area vector.
Step 2: The electric flux through a surface is also given by:
\[ \Phi_E = E A \cos \theta \] where \( E \) is the magnitude of the electric field, \( A \) is the area of the surface, and \( \theta \) is the angle between the electric field and the normal to the surface.
Step 3: The dimensions of electric flux can be derived by considering the units of electric field (\( \text{N/C} \)) and area (\( \text{m}^2 \)). The dimensions of electric flux are:
\[ \left[ \Phi_E \right] = \left[ E \right] \times \left[ A \right] = \left[ \frac{\text{N}}{\text{C}} \right] \times \left[ \text{m}^2 \right] \] Using the dimensions of force (\( \text{M L T}^{-2} \)) and charge (\( \text{A s} \)), the dimensions of electric flux are:
\[ \left[ \Phi_E \right] = \text{M L}^3 \text{T}^{-3} \text{A}^{-1} \]