## Wednesday, September 21, 2016

### Magnetism Inverse Square Law and Torque

Magnetism is the property of certain type of material because of which they are able to attract some other kind of materials like iron and copper. There are some natural magnetic materials that can do that but to use the property practically magnets were made artificially.

Bar magnets are popular artificial magnets and they are in bar shape with north and south poles at the edges. The distance between two poles is called length of the magnet and it is bit less than the geometrical length of the magnet.

There will be a field around every pole up to where it can influence the surroundings and the field is called magnetic field. Magnetic line of force is the imaginary path followed by a unit north pole and they start from North Pole and move towards South Pole of the magnet. They are closed loops. They travel from South Pole to North Pole inside the magnet. Two lines of force never intersect with each other. The tangent drawn at any point of the line of force gives the direction of the magnetic field at any given point.

If they intersect with each other, at the point of intersection, we can draw two tangents and hence it is supposed to have two directions at that point. It is not practically possible for a field to possess two directions at a given point simultaneously and hence two lines of force never intersect with each other.

If the strength of the magnetic field is high, we can find more number of magnetic lines of force around it. If the magnetic field is uniform, magnetic lines of force around that field will be parallel to each other.

Number of magnetic lines of force in a given area is called magnetic flux and magnetic flux per unit area is called magnetic field induction or magnetic field strength. It is measured with a unit weber per meter square.
Torque experienced by a bar magnet in a uniform magnetic field

Every bar magnet do have two poles called north and south poles. Their pole strength is same in magnitude but opposite in nature. Each pole when placed in a magnetic field experience a force in a specified direction. Thus the magnet has a pair of forces acting on its poles in opposite direction at its different ends. This produce a turning effect in the magnet and it is called torque. We can find the torque as the product of any one force and the perpendicular distance between them.

We can draw a diagram to represent the force and torque as shown in the diagram below.

Let us assume each pole of the bar magnet has pole strength m and let it is placed in a uniform magnetic field of field strength B. Hence each pole experience a force and the two forces are acting on two different edges of in opposite direction. They together turn the bar magnet in the anti-clock wise direction and hence there is a torque acting on it.

We can find the value of perpendicular direction basing on the angle made by the magnet with the field as shown in the diagram below.

If the angle between the field and the bar magnet is zero, then the toque acting is zero and if they are perpendicular to each other, magnetic fields torque is maximum.

Torque can be defined as the magnetic moment of a bar magnet when it is placed in a uniform magnetic field of field strength one unit and it is perpendicular to the field.

Force between two poles

It is experimentally observed that similar poles experience a force of repulsion and opposite poles experience a force of attraction. The magnitude of force of attraction or repulsion is directly proportional to the product of the pole strengths and is inversely proportional to the square of the distance of the separation. This force depends on the media between the two poles and two study that, we introduce a term permeability. It is the measure of nature of the medium that how good or bad the medium is in passing the magnetic field through it.

Pole strength is measured with a unit ampere-meter. Pole strength of a pole is said to be one unit when two identical poles separated by unit distance of separation in vacuum experience a force in the order of negative 7 orders.

If the medium is different between the two poles, the force between them changes and we shall use the permeability of that medium. We can define relative permeability as the ratio of permeability of the medium to the permeability of the vacuum.

Magnetic field induction varies on axial and equatorial line. The line passing through both the poles and also along the center of the magnet is called axial line. The line passing through the center of the magnet and perpendicular to the axial line is called equatorial line.

It can be proved that the magnetic induction on axial line is double the induction value on the equatorial line at the same distance.

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