Originally Posted by **ohm** In a textbook , in case of motional emf this is given
Case 1 plane is taken as plane of paper and direction of magnetic field is perpendicular to the plane of paper and inward. A conducting rod is moving perpendicular to the field but it's direction is not perpendicular to its length. Then the flux linked with area generated by the motion of rod in time t is
Flux=BA cos0 I.e angle between field and area vector is taken as zero degree.
Case 2. Again in the same plane a conducting rod is rotating in anticlockwise direction. The flux linked with area generated by
Flux= BAcos180 I.e. angle between area vector and field is taken as 180 degree.
Why angles are different? |

The area vector tells you about the magnitude of the area of a surface and the orientation of it.

The flux generated depends on the

*relative* orientation of the field and the conducting area. It is the dot-product of the two quantities.

The dot-product makes use of the cosine function. This function is even, which means that it has a symmetric property such that for problems involving the comparison of two orientations, the results work out naturally, so you don't have to worry about "getting it wrong" by making the area vector point one way or the other.

For example; consider a field perpendicular to the surface so the area vector is parallel to the magnetic field strength. If we consider the two orientations of the area vector, we have

$\displaystyle \cos 0^o = 1$

$\displaystyle \cos 180^o = -1$

So the magnitude is the same in both cases. If your area vector is pointing in the opposite direction, the flux will be expressed relative to the area vector's orientation, so you'll get a negative flux in one orientation and a positive one in the other, indicating that there's only one direction in which the flux is travelling in. It works out naturally.