why is Bcos30 the result of the first dot productSolutionGen

why is Bcos30 the result of the first dot product.

Solution

Generally current ,charge and flux like quantities are represented with density of that particular quantity.density of flux is the flux passing through the unit area normal to the direction of flux passing.that is we consider a normal surface to the flux passing to calculate the flux densitty.In this problem direction of normal surface is fixed(physical dimension of circular loop) so we have to take the effect of flux component on this surface element.Given that flux density is makes an angle of 30 degree with the normal to the surface.so the flux component in the direction of normal to surface=Bcos30.(here physical dimension of surface area is fixed because we intentionally calculating the flux linkages inside current loop i.e in the axial direction of circular loop)