The electric flux is maximum when the angle between the electric field vector and the area vector is 0 degrees.
Explanation
Electric flux, denoted by ΦE, is a measure of the electric field passing through a given surface. It is defined as:
ΦE = ∫ E ⋅ dA
where:
- E is the electric field vector.
- dA is the differential area vector, which is a vector perpendicular to the surface with a magnitude equal to the area.
The dot product can be expanded as:
ΦE = ∫ E dA cos θ
where θ is the angle between the electric field vector E and the area vector dA.
Maximizing Electric Flux
To maximize the electric flux, we need to maximize the term cos θ. The cosine function reaches its maximum value of 1 when θ = 0°.
Therefore, the electric flux is maximum when:
- θ = 0°
- The electric field vector E and the area vector dA are parallel (pointing in the same direction).
- The electric field is perpendicular to the surface.
Visual Representation
Imagine a flat surface and electric field lines. When the electric field lines are perpendicular to the surface, the maximum number of lines pass through the surface, resulting in maximum flux. If the surface is rotated such that the angle between the field lines and the normal to the surface increases, fewer field lines pass through, and the flux decreases. When the surface is parallel to the field lines (θ = 90°), no field lines pass through, and the flux is zero.
Summary
Electric flux is maximized when the electric field is perpendicular to the surface, meaning the angle between the electric field vector and the area vector is 0 degrees.
