Magnetic field lines represent regions of space that have the ability to enact forces upon charged particles in motion. Likewise, a stationary charged particle will experience a force from a nearby magnet when it is put into motion. Time and time again, we will see that the magnitude of the force enacted by a magnetic field is proportional to the magnetic flux density ( B ) of the magnet in question. A B-field describes the amount of magnetic flux ( ɸ ) that passes through an area perpendicular to it. Consider the magnetic cores in the diagrams below:
It is easy to see that the lattermost image contains more magnetic lines of force than the previous one. We would be mistaken, however, to conclude that flux density is greater in the second diagram!!!
Q: What is the magnetic flux density of the magnetic cores above? Assume that each dot is representative of a micro-Weber of flux.
A: Let’s begin by counting the number of flux lines present in each area:
Diagram 1: 49 µW
Diagram 2: 72 µW
In order to make flux density determinations, we must now calculate the area encompassed by each magnetic core:
A = length x width
A1 = ( 0.025 m )2
A1 = 6.25 x 10-4 m2
A2 = ( 0.025 m )( 0.05 m )
A2 = 1.25 x 10-3 m2
Finally, we divide the number of flux lines in each diagram by the area each diagrams encompasses:
B = ( ɸ / A )
B1 = ( 49 µW / 6.25 x 10-4 m2 )
B1 = 7.84 x 10-2 Wb / m2 = 7.84 x 10-2 T
B2 = ( 72 µW / 1.25 x 10-3 m2 )
B2 = 5.76 x 10-2 Wb / m2 = 5.76 x 10-2 T
RENAISSANCE PHYSICS 