Question

What is the definition of area vector A? Give an example of a commonly used application of A. Please explain every step taken as you solve the problem and don't skip any steps.

Answer 1

Area vector is simply the magnitude of area of any surface accompanied by its direction. It is to ensure remembered that area vector always lie perpendicular to the surface i.e. it makes an angle of 90° with the surface.

It's application can be easily seen in Gauss law of electrostatics or Faraday's law of electromagnetic induction.

✓In the Gauss law of electrostatics, E×A×cos (theta) = q/₀

Where angle (Theta) represents the angle between electric field (E) and the area vector (A)

✓similarly, in Faraday's law of electromagnetic induction,

Induced EMF = B×A×cos (theta)

Where , angle (theta) represents the angle between the magnetic field (B) and the area vector of the loop (A)