PHYSICS

tf Magnetism and Matter s



s Some commonly known ideas about magnetism
i. The earth behaves like a magnetic with the magnetic field pointing approximately from the geographical south
to north.
ii. A bar magnet when suspended freely points in the North-South direction. The tip which points to the
geographical north is called the north pole of the magnet and that which points to the geographical south is
called the south pole of the magnet.
iii. Like poles of the magnet repel and unlike poles attract.
iv. Magnetic monopoles do not exist. If we cut a magnet in half, we end up with two smaller magnets with both
north and south pole.
v. It is possible to make magnets out of iron and its alloys


s
Bar magnet
A bar magnet has two poles. One pole is designated as the North pole and the other as the south pole. When iron
filings are sprinkled around a bar magnet, they are arranged in a pattern similar to the one seen around a current
carrying solenoid.

s Magnetic field lines (PYQ 2019)
- Magnetic field lines for a bar magnet or a current carrying solenoid form closed loops, this is because magnetic
monopoles do not exist.
- Tangent to a field line at a point gives the direction of the magnetic field at that point.
- The greater the density of field lines in a region, the greater is the magnitude of the magnetic field in that region.
- Magnetic field lines do not intersect. This is because, at the point of intersection there will be two tangents which
means that the magnetic field at that point will have two directions, which is not possible.




(i) Bar magnet (ii) solenoid



Note: 1. For a bar magnet (or a current carrying solenoid) the direction of magnetic field is from the North pole to
the South pole outside the magnetic and from the south pole to the north pole inside the magnet.
2. Unlike in electrostatics, the magnetic field lines do not indicate the direction of force on a moving charge.


s
Bar magnet as an equivalent solenoid
Ampere hypothesized that all magnetic phenomenon are due to circulating currents. The similarity between
magnetic field lines produced due to a bar magnet and a current carrying solenoid suggests that a bar magnet may
be thought of as a large number circulating atomic currents in analogy with a solenoid.




Ann
Titian .

, Consider a solenoid of length 2L and radius a carrying current I, having no of turns per unit length as n. Let us
calculate the field at a point P on its axis at a distance r from its center. Consider a differential element of thickness
dx a distance x from the center. It consists of n.dx turns. We know the expression for field due a to a circular element
at a point on its axis-




Z l


-
l




For




l

- l




( m = NIA)
r

:




This is also the magnetic field for a bar magnet a point far on its axis (obtained experimentally). Thus, a bar magnet
and a solenoid produce similar magnetic fields. The magnetic moment of a bar magnet is thus equal to that of an
equivalent solenoid which produces the same magnetic field.



S
Magnetic pole strength/ Magnetic charge (qm)
1. It is called magnetic charge and is analogous to electric charge| SI unit- A m (ampere-meter)
2. It depends on area of cross-section and intensity of magnetization
3. North pole has a magnetic charge +qm and south pole has -qm
4. Magnetic moment of a bar magnet of length 2L can be written as –


5. Consider a solenoid of length L, current I and n no of turns per unit length. Its magnetic moment can be
written as-

Also-


Equa+ng both-




6. The magnetic field strength due to qm at a distance can be written as-

s
Dipole in a uniform magnetic field (PYQ 2013)
Consider a magnetic needle of magnetic moment m and moment of inertia I kept in a magnetic field B making an
angle θ with the field. The needle experiences a torque which is given by-
Ann

Titian . .