# Magnetic field and Magnetic force

‘Opposites attract’. You must have heard this phrase quite often. But why do opposites attract? Where did this phrase originate from? This phrase comes from the magnet and its magnetic field. The opposite poles of a magnet attract each other. In actuality shouldn’t opposite poles repel and like poles attract each other? Isn’t it? ‘No’ you say. Well, then let us prove your theory below.

Table of content

## What is Magnetism?

A bar magnet attracts iron objects to its ends, called poles. One end is the north pole, and the other is the south pole. Magnetism is the phenomena arising from the force caused by magnets that produce fields which attract or repel other metallic objects. It is caused because of electrically charged particles. The force acting on the electrically charged particles in a magnetic field depends on the magnitude of the charge, the velocity of the particle, and its strength. Magnetism states that:

1. Opposite poles attract.
2. Like poles repel.

If two bar magnets are brought close together, the like poles will repel each other, and the unlike poles attract each other.

### Magnetic field

When a positively charged particle moves in a uniform magnetic field, then the direction of the velocity of the particle is perpendicular to the field. The magnetic force always acts in a direction perpendicular to the motion of the charge.The space or the region around a magnet within which magnetic force is exerted on other magnet is called as the magnetic field.

To locate the magnetic field of a bar magnet, we use a magnetic compass. When a magnetic compass is kept away from the magnet, it doesn’t deflect. When a magnetic compass is brought closer to the magnet it deflects. If the magnetic field lines are very close to each other in a particular region, then the strength of the magnetic field is very strong, and if the magnetic field lines are far away then the magnetic field is very weak.

It is expressed in the unit Tesla.

### Magnetic force

The magnetic force is the force of attraction or repulsion that arises between electrically charged particles due to their motion  The magnetic force between two moving charges may be described as the force exerted upon their charge by the magnetic field created by the other. This force causes the magnets to attract or repel one another.

Examples of magnetic force is a compass, a motor, the magnets that hold stuff on the refrigerator, train tracks, and new roller coasters. All moving charges give rise to a magnetic field and the charges that move through its regions, experience a force. It may be positive or negative depending on whether the force is attractive or repulsive.The magnetic force is based on the charge, velocity and magnetic field of the object.

## Force on a moving charge

If a charge moves through a magnetic field at an angle, it will experience a force. The equation is given by
F = qvB sin θ, where q is the charge, B is the magnetic field, v is the velocity, and θ is the angle between the directions of the magnetic field and the velocity. The motion of charge q moving with the velocity v in a magnetic field, has a force acting on it and this force is:

1. proportional to the charge q
2. proportional to the velocity v
3. perpendicular to both v and B
4. perpendicular to sinθ where θ is the angle between v and B

This is written as,

$$\vec{F} = q \vec{v} \times \vec{B}$$

## Right-Hand Rule

The direction of the force (F) can be found from the Right-hand rule.

It applies to the devices that use motion in a magnetic field to generate currents.

• Point your index finger along the direction of motion of charge v
• Rotate your middle finger away from your index finger between v and B
• Hold your thumb perpendicular to the plane formed by your index finger and middle finger
• Your thumb will then point in the direction of the force (F) if the charge q is positive.

(Source: engineering.com)

## Solved Example For You

Q.Determine the magnetic force of 50 C charged particles moving with the velocity of 3m/s in a magnetic field of 1T? The direction of its field is same as the path of the second particle.

Sol: Given parameters, q= 50C, v= 3m/s and B= 1T
Since the path difference of the second particle is same as its field’s direction,
Therefore, θ=0°
The magnitude force formula is
F= q v B sinθ = 50×3×1× sinθ =0

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