**NEET Physics Notes Magnetism-Bar Magnet**

**Bar Magnet**

**Bar Magnet**

In magnetism, isolated magnetic poles, similar to isolated electric charges in electricity, have yet not been found to exist.

The simplest magnetic structure is the magnetic dipole characterised by a magnetic dipole moment M.

A bar magnet exhibits two important properties, namely

- the attractive property
- the directive property

A bar magnet may be viewed as a combination of two magnetic poles, North pole and South pole, separated by some distance. The distance is known as the magnetic length of the given bar magnet. If m is the pole strength and 2l the magnetic length of the bar magnet, then its magnetic moment is M = m(2I). Magnetic moment is a vector whose direction is from S-pole towards N-pole. SI unit of magnetic pole strength (m), is ampere metre (Am) and of magnetic dipole moment (M) is ampere metre^{2} (Am^{2}).

If a bar magnet is broken, the fragments are independent magnetic dipoles and not isolated magnetic poles.

**Magnetic Field due to a Bar Magnet**

A bar magnet has a magnetic field around it. Magnetic field is mathematically measured by a vector term B, whose SI unit is 1 tesla (IT).

The magnetic field in free space, at a point having distance r from the given bar magnet (or magnetic dipole).

and the direction of B is the same as the direction of M. For a short dipole (or for a far away point on the axis) when r > > l, the above relation is simplified as

Along the equatorial line of a magnetic dipole, the magnetic field B in free space is given by

If **r > > I,** the relation is modified as

However, along the equatorial line, the direction of B is opposite to that of M.

In general, in a direction making an angle θ from with the magnetic axis, the magnetic field is given by

In these relations, is a constant having a value of and it is known as the magnetic permeability of free space.

For solenoid where n is number of turns of solenoid and i the current through it.

**Magnetic Field Lines**

A magnetic field line is a smooth curve in space, tangent on which, at any point, gives the direction of the magnetic field at that point.

Magnetic field lines starts from North pole of a magnet and end at the South pole. However, within the magnet, they move from the South pole to the North pole and form closed loops.

Number of two magnetic field lines can ever intersect each other.

Relative closeness of magnetic field lines at a given place gives the idea of magnetic field strength at that place. If field lines are close to one another, it shows a stronger field and vice-versa.

**Magnetic Dipole in a Magnetic Field**

A magnetic dipole when placed in an uniform magnetic field, does not experience any net force. However, it experiences a torque given by

where, θ is the angle from the magnetic field, along which the dipole has been placed.

Work done in rotating a magnetic dipole in an uniform magnetic field from an initial orientation θ_{1} to the final orientation θ_{2} is given by

Potential energy of a magnetic dipole placed in a uniform magnetic field, is given by

Thus, potential energy U_{B} = – MB = minimum when dipole is parallel to B and U_{B} MB = maximum when dipole is anti-parallel to B.

The magnetic compass (needle) of magnetic moment M and moment of inertia I and allowing it to oscillate in the magnetic field. Then, its time-period is