Sunday, September 25, 2016

Magnetic Components of the Earth Magnetic Field and Potential Energy

The earth has a strong magnetic field around it. It is because the earth itself behaves like a strong magnet with its north and south poles of the magnet in reverse with the geographic north and south of the earth.

The entire earth magnetic field can be resolved into horizontal and vertical components. Magnetic meridian is a vertical plane that connects the north and south of the earth.

The angle between magnetic meridian and geographic north and south is called angle of declination. Its value at the equator angle of declination is approximately seventeen degree.

The angle between horizontal component and the vertical component of the earth magnetic field is called angle of dip or inclination. This value varies between zero and ninety degree. At magnetic meridian it is zero degree and at the poles its value is ninety degree. The lines joining the points with same dip are called isoclinical lines.

Apparent dip

The angle made by a magnetic needle with the horizontal component of the earth magnetic field is called apparent dip. We can get to a conclusion as shown in the diagram below.

Intensity of the magnetic field is defined as the magnetic field strength per unit permeability of free space or medium. It is a vector quantity and has similar direction of magnetic field strength.

Intensity of Magnetization is defined as the magnetic moment per unit volume.

Magnetic susptability  is defined as the ratio of intensity of magnetization to the magnetic intensity. It is a scalar quantity and it has no units and dimensions.

We can find the relation between susptability and relative permeability as shown in the diagram below.We can express the total magnetic field strength as the vector addition of horizontal and vertical components of the earth magnetic field. By simplifying it further we can get the relations as shown in the diagram below.

Potential energy of a bar magnet

Let us assume a bar magnet placed in the magnetic field. We need to do some work in rotating it from one position to other. This work done will be stored in the format of potential energy after the work is done.

The small amount of work done is defined as the dot product of torque experienced by the bar magnet and the small angle it got turned. To get the total work done, we shall integrate the equation and certain limits are applied. Thus we are able to measure the total work done and that itself is equal to the potential energy of the system.

Its value varies depending on the angle from where to where it is turned. Its value vary if we are starting rotating the magnet from the original or the earth magnetic field itself. We can also measure the work done if we are moving in a turn around way that is rotating it in opposite direction.

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