Properties of Magnetic Field Lines Around a Bar Magnet
Magnetic lines of bar magnet
Magnetic lines of force of a magnet shows the direction in which a magnetic material will be aligned when placed at the location. Magnetic field lines for a bar magnet are as shown in the diagram.
Properties - Magnetic lines of force
Properties of magnetic lines of force are:
They are continuous closed curves.
They originate from the North Pole and terminate at the South Pole.
Two lines do not intersect each other.
They are crowded where the magnetic field is strong, i.e. near the poles.
Magnetic field follows superposition principle
The magnetic field of several sources is the vector addition of magnetic field of each individual source. Thus it follows the superposition principle.
Properties of magnetic fields of lines
Magnetic field lines are imaginary lines that represent magnetic fields. It gives direction of magnetic force. An advantage of using magnetic field lines as a representation is that laws of magnetism and (electromagnetism) can be stated using concepts like 'number' of field lines through a surface.
Magnetic field lines are like streamlines in fluid flow, they represent something continuous, and a different resolution would show more or fewer lines. Various phenomena have the effect of displaying magnetic field lines as though the field lines were physical phenomena. For example, iron filings placed in a magnetic field, form lines that correspond to field lines. Field lines can be used as a qualitative tool to visualize magnetic forces.' Unlike' poles of magnets attract because they are linked by many field lines, 'like' poles repel because their field lines do not meet, but run parallel, pushing on each other.
The net magnetic flux through a closed surface is zero
The contribution to magnetic flux for a given area is equal to the area times the component of magnetic field perpendicular to the area. For a closed surface the number of magnetic field lines entering the surface is equal to the number of field lines exiting it.Thus the sum of magnetic flux is always equal to zero.
Magnetic Field strength due to bar magnet
Consider a bar magnet of length 2l and pole strength m. Suppose a point P on the axis of the magnet at a distance r from its center. (r-l) is the distance of P form the N-pole of the magnet. The magnetic field intensity at P due to the north-pole of the magnet is B1=4πr2μom B1=4π(r−l)2μom which is directly away from N-pole. Since the south of the magnet is at a distance r + l from P, so magnetic field intensity at P due to S-pole is B2=4π(r+l)2μom which is direct towards, the S-pole of the magnet. The magnetic field intensity B at P is the resultant of these two fields B=B1+(−B2) B=B1−B2) =4πμom×[(r−l)21−(r+l)21] =4πμom×(r2−l2)24lr =4π(r2−l2)2μo2Md
Example - Magnetic filed strength due to a bar magnet
A magnet is 10 cm long and its pole strength is 120 CGS units (1 CGS unit of pole strength=0.1Am). Find the magnitude of the magnetic field B at a point on its axis at a distance 20 cm from it. Solution: The pole strength is m=120 CGS units = 12Am. Magnetic field is 2l=10cm or l=0.05m. Distance from the magnet is d=20cm=0.2m. The field B at a point in end-on position is: B=4πμ0(d2−l2)22Md=4πμ0(d2−l2)22mld=(10−7ATm)[(0.2m)2−(0.05m)2]24×(12Am)×(0.05m)×(0.2m)=3.4×10−5T