Bar magnet as an solenoid

A magnet is an object that produces a magnetic field, sometimes it occurs naturally, and sometimes they are made. The magnetic field is responsible for the unique properties of the magnet, and it is invisible. The materials that can be magnetised (attract towards magnet) are called ferromagnetic materials such as iron, cobalt, nickel etc. There are two main types of magnet: Permanent magnet, Temporary magnet. Permanent magnets maintain their magnetic properties for an extended time, e.g. Bar magnet, horseshoe magnet, etc. Temporary magnets simply act as a magnet until they are placed in strong magnetic fields, e.g. electromagnet etc.

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Magnets have some other properties, so we have to consider all things first before understanding Bar magnet as an equivalent to a solenoid.

Bar magnet

A bar magnet is rectangular in shape made up of iron steel or other ferromagnetic material that shows a permanent magnetic property. Sometimes a bar magnet is also a naturally occurring magnet. It has two poles: the North pole and the South pole. When a bar magnet is freely suspended in the air, its north pole points towards the geographical north direction and its south pole points towards the geographical south direction. That’s why it is used as a compass.

Properties of Bar magnet

• It always points towards the north-south direction when freely suspended.

• There is a repulsive force act when the north poles of two bar magnets are brought together. The same thing happens with the south pole also.

• If a bar magnet is broken into two or more pieces, then every piece of magnet has its north-south pole. It means you can’t isolate the poles.

Electromagnet

An electromagnet is a type of magnet in which the flowing of an electric current induces the magnetic field. The electromagnet consists of wire wound into the coil. When the electricity passes through the coil, a magnetic field is generated around the coil, concentrated towards the coil’s centre. When the current turns off, the magnetic fields disappear. Electromagnet always requires the current supply to work like a magnet and maintain its magnetic field. The main advantage of the electromagnet is that you can control the magnet and the strength of its magnetic field by changing the current in the wire.

An electromagnet is generally used as a motor, generator, solenoid, loudspeaker etc. In factories, electromagnets lift and move heavy iron objects such as scrap iron and steel material.

Solenoid

A solenoid is a type of electromagnet, the purpose of which is to induce a controlled magnetic field through a coil wound into a tight-packed spiral wire. The term solenoid was chased in 1823 by André-Marie Ampère to designate a spiral coil. The solenoid also refers to any device which converts the electric current into the magnetic field and uses the magnetic field to create a linear motion.

The solenoid is a wire coil, which is made of a soft iron-like substance. A solenoid is a coil whose length is virtually greater than its diameter. The spiral coil does not necessarily need to revolve around a straight-line axis. 

If the number of turns per unit length increases, then the intensity of the magnetic field also increases, so the number of turns is directly commensurable to the magnetic field.

Bar magnet as an equivalent solenoid

The unity of magnetic field lines of a bar magnet and a solenoid is suggested that a bar magnet may be thought of as a large number of circulating current analogies with a solenoid. Simply cutting a bar magnet is the same as cutting a solenoid because both form a new magnet and a solenoid independently but with weaker magnetic properties. The magnetic fields are, as usual, arising from one face of the solenoid and entering into the other face.

Before demonstrating the axial field of a solenoid, we have to recall the magnetic dipole moment m associated with the current loop was defined to be m=NIA, where N is the number of loops, I is current, and A is the area vector.

The magnetic field produced by a solenoid is the same as that produced by a current-carrying solenoid. To demonstrate this, we will calculate the axial field of the current-carrying finite solenoid.

Then we assume  for a solenoid that:

n = no. in of turns per unit length; 

a = radius of solenoid;

2l = length of solenoid with centre O;

I = current flowing in the solenoid.

To do this, consider the a circular elements of thickness dx of the solenoid at a distance x from its centre.Hence it consists of ndx turns.

dB = 0n dx Ia22[(r -x)2 + a2]3/2

The magnitude of the total magnetic field is attained by casting over all the elements — in other words by integrating from x = – l to x = + l. Therefore:

B = 0 nIa22-lldx[(r – x)2 + a2]3/2

This integration can be done by trigonometric negotiation. Note that the range

of x is from – l to + l. Assume the far axial field of the solenoid, i.e.,r >> a and r >> l. Also the denominator is approached by:

[(r -x)2 + a2]3/2 = r3

So that , 

B = 0 nIa22r3-lldx

B =  0 nI2 2la2r3

The magnitude of the magnetic moment of the solenoid is, m = n (2I) l (a2) 

Therefore,

B =  0 4 2mr3

It is also the bar magnet’s experimentally obtained distant axial magnetic field. As a result, a bar magnet and a solenoid produce similar magnetic fields. The magnetic moment of a bar magnet is equal to the magnetic moment of an original solenoid that produces the same magnetic field.

It is clear from the given expression that the magnetic moment of a bar magnet is equal to the magnetic moment of an equivalent solenoid that produces the same magnetic field.

Hence it is proved that both have the same magnetic field intensity. If the intensity is the same, the power is also the same, so we can say that the bar magnet is equivalent to a solenoid.

Conclusion

We learn about the Magnet and type of Magnet; Permanent magnet and Temporary magnet. Bar magnet and its properties, which helps find the relation to the magnetic fields and how they work when placed between the electric fields.

We also know about the Electromagnet and its working. We also saw how the bar magnet is equivalent to a solenoid when placed in the same electric field. Also, they produce the same amount of magnetic field. Factors that affect the electricity of electromagnets are the character of the centre material, the strength of the current passing via the centre, the variety of turns of wire at the centre and the shape and length of the core.