Question

The magnetic flux through a surface is defined as Phi = BAcos(theta). At what angle is the magnetic flux (a) amaximum and (b) minimum.

Please show work.

Answer 1

a) when theta = 0 degrees

b) when theta = 90 degrees

Answer 2

a> max at theta=0 degree

b> min at theta=90 degree

Answer 3

for max magnetic flux, cos should be maximum which can be 1 at 0 deg.

for minimum cos has to be 0 (as -1 would imply same amount of flux but in reverse direction)

hence angle is 90 deg

Answer 4

sometimes the scientific concepts get confused. Seems the word flux also has brought such a dilemma. Any way the word 'flux' both in electric field and magnetic field means the lines of force.
The most importance is consideration of either magnetic or electric lines of force linked with a given area. That is why we get the expression for flux in both the fields as the product of electric field intensity and area in case of electric field and the product of magnetic field induction and the area.
But the same symbol phi is used for both electric flux and magnetic flux. Any way the unit for electric flux will be Nm^2C^-1. And that for magnetic flux is weber.
Here flux is scalar. But both field are vector. Hence we have to consider area too, to be a vector. Hence the area vector will always be normal to the plane area. Thus flux phi = E . A in case of electric field and phi = B . A in case of magnetic field.
We know dot product of vectors would have cosine of the angle between the two vectors.
So phi= BAcos theta. Theta is the angle between the B vector and A vector.
If one loop is there then phi= BAcos theta. If there be N turns then the flux gets multiplied by N.
Hence phi = N B A cos theta.
If B and A are parallel, ie if lines of force pass through the plane area at right angles then theta is 0 and so cos0 = 1. So the magnetic flux phi = N B A. ie maximum.
In case N = 1, B = phi/A
So magnetic field induction is also defined as magnetic flux density. Usually density is measured as the quantity per unit VOLUME.
Here the density is measured as the quantity per unit AREA. ie surface density.
So unit for magnetic field induction is also known to be weber/m^2 and hence magnetic fluxdensityy.One important point to be notified that in case of magnetic field we use the term field INDUCTION and in case of electric field we use the term field INTENSITY.

Answer 5

flux = BA cos theta

theta is the angle between area of the lopp with field more precisely normal of the loop

i.e when Normal is hel parallel to the field large amouont field acts on the area of loop thus givening rise to maxmum flux ,t his is at zero deg

when normal of tle loop is held parallel to the field, least field acts on least area giving rise to mimimun flux. so this takes place at theta = 90 deg

is acted upon by

flux will be maximum when theta = 0 as cos 0 =1

and minimum whem theta = 90 as cos 90=0