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# Magnetism Formula

Magnetism is the physical phenomenon that is propitiated by the magnetic fields. The elementary particle’s magnetic moments and electric currents are generating the magnetic fields. The ferromagnetic materials are greatly attracted by the magnetic fields. Thus these can be magnetized easily towards the permanent magnets. Ferromagnetic substances are limited such as cobalt, nickel, iron and their alloys. The magnetic state of a material is dependent on temperature and some other variables such as the magnetic field and pressure. This topic will explain the magnetism formula with examples. Let us learn it!

## Magnetism Formula

### Definition of Magnetism:

Magnetism is referring to a group of natural phenomena in which certain metals display the property of attraction. These metals can be naturally occurring in rock formations as well as electrical and nuclear functioning.

Magnetic properties were first discovered and written about as early as AD 20. However, Aristotle described the properties of magnets to the contemporary of his without having the right terminology behind the science. There are two main sources of magnetic behavior, both of which are used for the creation of “permanent” magnets.

These magnets usually involve the coil of wire wrapped securely around some metal object, connected with some power source. This type of magnet is referred to as electromagnetism. Electromagnets are also used in many devices for communication as well.

We can consider the magnetic field surrounding a magnet. A magnet attracts the small pieces of iron even form a certain distance. Therefore, the magnetic force, like electric force and gravitational force, acts at some distance. This idea of a force involves the concept of a magnetic field.

The force that one magnet exerts on each other may be considered as the interaction between them under the magnetic field. A straightforward method to describe the magnetic field around the magnet is to draw field lines around it.

Therefore, the magnetic force is the result of electromagnetic force and is caused due to the motion of charges. We may term them as moving charges surround itself with a magnetic field.

### The formula for Magnetism:

1. The magnetic field of straight current-carrying wire

B=$$\frac{\mu_0 I}{2\pi d}$$

Where,

 B strength of the magnetic field d distance I current in wire $$\mu_0$$ the permittivity of free space

1. Magnetic Force:

The formula is,

$$F=q[E(r)+v\times B(r)]$$

Also, we can compute the magnitude of the magnetic force by:

$$\underset{F}{\rightarrow}=ILB\sin \theta \widehat{n^}$$

Where,

 F magnetic vector I current magnitude L length vector B magnetic field vector $$\theta$$ the angle between length and magnetic field vectors (radians) n cross product direction vector (unitless)

## Solved Examples

Q.1: The direction of the current in copper wire with a current of 6 A through the uniform magnetic field. It has the strength is 2.20T. The direction of the magnetic field is upward-left with an angle of $$\theta$$ of value $$\frac{3\pi}{4}$$ radians from the current direction. Compute the magnitude and direction for the magnetic force acting on 0.1 m length of the wire?

Solution:

Applying the formula, we get:

F = $$(6.00\, A)(0.100\, m)(2.20\, T)\sin(3\pi /4\,radians)$$

F = $$(6.00\, A)(0.100\, m)(2.20\, T)(1/\sqrt{2})$$

F = $$(6.00\, A)(0.100\, m)(2.20\, \frac{kg}{A\cdot s^{2}})(1/\sqrt{2})$$

F = $$(6.00)(0.100\, m)(2.20\, \frac{kg}{s^{2}})(1/\sqrt{2})$$

F = $$(6.00)(0.100)(2.20)(1/\sqrt{2})\,kg\cdot m/{s^{2}}$$

F $$\simeq 0.933\,\,kg\cdot m/s^2$$

Thus, the magnitude of the force will be 0.933 N. We may use the “right-hand rule” to find the direction of the force, which will be out of the page.

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