Bar Magnet as An Equivalent Solenoid

For understanding how the bar magnet is becoming equivalent to the solenoid, it is extremely important to understand the bar magnet and solenoid and the similarities and differences between them. The bar magnet is a rectangular or square piece of an object that is made from iron or steel that is having permanent magnetic properties with the two poles of south and north. Whereas, the solenoid is a coil that is having a greater length than its diameter, and it is the type of an electromagnet that is used for producing the controlled magnetic fields by the passing of electric current through it.

By the calculation of the axial field of the finite solenoid that is carrying a certain amount of current, it is possible to demonstrate a bar magnet as a solenoid. Let consider a solenoid that is having radius a and length 2l, and n is the number of turns per unit length in which current is passing through the solenoid. By using this above condition, it can be calculated that the magnetic moment of a bar magnet and magnetic moment of the solenoid are equal.

The magnetic field arising due to turns in the coil, at solenoid’s axis, can be given by

The magnitude of the total field can be obtained by summarizing all elements. Thus,

By using the trigonometric substitutions, the integration can be done. The denominator can be approximated by the following

Here, if the magnitude of the magnetic moment of the solenoid is m, then

From the above expression, it is clear that the magnetic moment of both solenoid and bar magnet is equal, which are produced by the same magnetic field.

Similarities Between Solenoid and Bar Magnet

  • Both the solenoid and bar magnet have directive and attractive properties as they can align themselves in the external magnetic field.
  • For both of them magnetic field is same at the axial point.
  • The magnetic moment for solenoid and bar magnet is also same.

Differences Between Bar Magnet and Solenoid

  • The solenoid is an electromagnetic magnet, whereas, the bar magnet is permanent one. It only acts like a magnet when there is passing of electric current through it.
  • If there is cutting of bar magnet into two equal halves, then both these pieces act like magnet. Whereas, if there is cutting of solenoid into two halves, then the filed will be weaker.
  • Poles of bar magnet are always fixed, whereas, the poles of solenoids can be altered. Strength of magnetic field of bar magnet is also fixed, but the strength of magnetic field of solenoid is dependent on electric current passing through it.


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