Magnetism

Magnets have played important role in the industry. If we inspect the different things around us, we could say that we are surrounded with magnets. The appliances we use at home, school, office or anywhere we could see them have magnetic parts on them which contributes to their different functions. The cars and other vehicles we are riding are made up of dozens of magnets that helps in the control of the different parts of the vehicles. Security systems and alarms are also equipped with magnets. Knowing the importance and the great role magnets provide, where do magnetic forces came from? What produces a magnetic field?

A material which produces a magnetic field is called as a magnet. An object which is made from a magnetized material and creates its own persistent magnetic field is known as a permanent magnet. These magnets are found to be exerting force to each other and to other materials like iron that are not magnetized. Based on experiments and observations, it was discovered that an unmagnetized iron rod becomes magnetized every time it is brought in contact with a natural magnet.

If electrical charges are described as positive, negative, and neutral, magnets are described through its magnetic poles. This is shown by the interaction of a permanent magnet and a compass, particularly the compass needle. A compass needle is an example of a magnetized iron. When a bar magnet, a magnet with a bar shape, is brought near a compass, and a bar magnet is free to rotate, one end will point to north. This end of the magnet is considered as the north pole or N pole and the other end is the south pole or S pole. Unlike poles attract each other. Like poles repel each other. The figures below show the interaction between two bar magnets as indicated by their poles.

When a magnet is broken into two, each end of the broken magnet will become poles. Unlike electrical charges, the north and south poles of a magnet always are in pair and cannot be isolated. That is, every time a magnet is broken, each broken magnet will still have north and south pole. Each piece will become a magnet with two poles and not two isolated or different poles of magnets. Refer to figure below. What matters is their magnetism. The smaller the piece, the weaker the magnetism.

Magnets can also attract other materials which contain iron but are not itself magnetized. In this case, the materials can be attracted to either pole of the magnet. Examples of these are nails sticking on a magnet, and the attraction between the magnet and the unmagnetized steel door of a refrigerator. The reason for the attraction is said to be due to the magnetic field produced by a magnet, and the unmagnetized material reacts to the magnetic field produced.

Magnetic Field

A magnetic field is produced by moving charges or current on its surrounding. It exerts force, \vec F to other charges moving or present in the field. Magnetic field is a vector quantity with symbol \vec B. It can be described by a magnitude and direction. The direction of a magnetic field depends on the direction of a compass needle would point and the magnitude depends on the strength of the magnetic force.

A Danish physicist named Hans Christian Oersted discovered the basic principle of electromagnetism which states that:

"Whenever electrons move through a conductor, a magnetic field is created in the region around the conductor."

Magnetic Field and Magnetic Forces on Moving Charges

1. The magnitude of the magnetic force is directly proportional to the magnitude of the charge. Two charges of different magnitude moving with the same velocity on the same field experience different amount of magnetic force. The one with greater charge would likely to experiences greater force that the one with smaller charge. For example, if 1 C and 2 C of charge is moving around the same magnetic field at the same velocity, the 2 C charged particle experiences twice as much as the force experienced by the 1 C charged particle.

1. The magnitude of the force varies directly as the magnitude or strength of the field. Magnetic force is stronger on stronger magnetic field. In the case of broken bar magnet, the smaller piece would have weaker magnetic field, thus, weaker magnetic force, while the longer field would have strong magnetic force and field. For example, if the magnitude of the field is doubled, like using two magnets instead of one, with constant charge and velocity, the magnetic force will also double.

1. The magnetic force depends on the particle’s velocity. The faster a charged particle moves, the stronger the magnetic force applied to it. Slower charged particle experiences lesser force. A charged particle at rest does not experience magnetic force.

1. The direction of the magnetic force is always perpendicular to the direction of both the magnetic field and velocity. It does not have the same direction as the magnetic field. The magnitude of the magnetic force is proportional to the component of the velocity perpendicular to the field. When the component of the velocity is zero, the force is also zero. The magnitude of the force can be expressed mathematically as

$$F = |q|vB = |q|v_{\perp} B \sin \phi$$     (1)

where $$|q|$$ is the magnitude of the charge and $$\phi$$ is the angle measured between the direction of $$\vec v$$ and the direction of $$\vec B$$.

 When a charge is moving parallel to a magnetic field, the magnetic force it experiences is zero. When a charge is moving at an angle $$\phi$$ to a magnetic field, it experiences a magnetic force whose magnitude is $$F = |q|vB = |q|v_{\perp} B \sin \phi$$. When a charge is moving perpendicular to a magnetic field it experiences a maximal magnetic force whose magnitude is $$F_{max}=qvB$$.

To find the direction of the magnetic force, we use the right-hand rule. First, draw the vectors  $$\vec v$$ and $$\vec B$$, tail to tail. Suppose your palm is the $$\vec v-\vec B$$ plane. Now, imagine turning $$\vec v$$ to the direction of $$\vec B$$. Considering a line perpendicular to the plane, curl your fingers around the line so that there’s a rotation from $$\vec v$$ to $$\vec B$$. The direction to which the thumb points pertains to the direction of the force on a positive charge. Below is the visual representation of the use of right-hand rule in determining the direction of the magnetic force.

 Right-hand rule for the direction of magnetic force on a positive charge moving in a magnetic field. Right-hand rule for the direction of magnetic force on a negative charge moving in a magnetic field.

This implies that the magnitude and direction of the force $$\vec F$$ exerted on a charge q moving with velocity $$\vec v$$ in a magnetic field $$\vec B$$ is given by the equation

$$\vec F = q\vec v \times \vec B$$     (2)

The above equation is valid for all moving charges, either positive or negative. The difference is that the direction of $$\vec F$$ if q is negative is opposite to that of $$\vec v \times \vec B$$.

When two oppositely charged particles of the same magnitude and velocity is moving at the same magnetic field, both will experience the same amount of magnetic force but with opposite direction.

Note that equation (1) gives the magnitude of the magnetic force and that $$\phi$$ is the angle between the direction of $$\vec v$$ and $$\vec B$$. We may take $$B \sin \phi$$ as the component perpendicular to $$\vec v$$ denoted as $$B_{\perp}$$. We can now write (1) as

$$F = |q|vB_{\perp}$$

The unit for the magnitude of the magnetic field B is tesla abbreviated as T. It is named after the prominent Serbian-American scientist and inventor Nikola Tesla.

$$1\; T = 1\; N/A \cdot m$$