# Is Magnetic Field And Magnetic Force Same: Different Aspects And Facts

Magnetic field and magnetic force go hand in hand. In this article, we will discuss the fascinating relationship between these two.

A magnetic field is an actual entity that fills up the space around a current-carrying conductor or moving charge, or magnet. In addition to this the force acted by a magnetic field upon a moving charged particle is magnetic force.

## How magnetic field is connected to magnetic force

To understand it more precisely, if we place a static charge in a magnetic field, the charge experiences no force, so to define a magnetic field, we take a charge q which is moving with velocity v in such a field [Fig. 1(a)]

If $F_{m}$ is the force exerted by the field on the moving charge, then it has been experimentally found that;

1. $F_{m}\propto v$
2. $F_{m}\propto q$
3. $F_{m}\propto v\sin \Theta$

If $F_{m}$ is the force exerted by the field on the moving charge, then it has been experimentally found that;

Combining the above three points, we obtain

$F_{m}= Bqvsin\Theta$ …………(1)

Here B is the proportional constant, and it gives the magnitude of the magnetic field. It is also known as magnetic flux density or magnetic field induction, or simply magnetic field. It is a pseudo-vector, and we denote it by B.

## When a magnetic field is exactly equal to magnetic force

If we consider q=1, v=1 and $\Theta$ = 90⁰

From equation (1), $F_{m}= B$

So here, we can say that the magnetic field at a point is thus equal to the magnetic force acting on a unit charge when it is moving with unit velocity in a direction perpendicular to the magnetic field.

In vector notation, $F_{m}= q(B\times v)$

Obviously, $F_{m}$ known as magnetic Lorentz force, is perpendicular to the plane containing v and B.

In case, $\overrightarrow{v}\perp \overrightarrow{B}$,$|\overrightarrow{v}\times \overrightarrow{B}|= vBsin90^{\circ}= vB$

In that case, $F_{m}= qvB$

As, $F_{m}= qvB$

$B= \frac{F_{m}}{qv}$

If  $F_{m}$ = 1N, q=1C and v = 1m/s

Then, $1T= \frac{N}{C(m/s)}$

$1T= \frac{N}{Ampere}$

The SI unit of B is called tesla(T)

So, the magnetic field at a point is thus said to be one tesla if a charge of 1 coulomb when moving perpendicular to the direction of the magnetic field with a velocity of 1 meter/second, experiences a force of 1 newton.

## Direction of magnetic field and magnetic force

Magnetic field does not flow in direction of its source that is current; instead, it flows normal to the direction of current. Additionally, the magnetic force act perpendicular to magnetic field.

Direction of magnetic field can be detected using right hand thumb rule. According to right hand thumb rule; If a current carrying wire kept in hand, then direction of thumb implies direction of current and direction of fingers indicates direction of flow of magnetic field.

## Example

If we take a bar magnet and bring it to an iron nail, at some point, the nail moves towards the magnet and sticks to it. Moreover, it remains there until we manually separate it from the magnet. So why does an iron nail stick to the magnet?

Reason behind is the force of attraction that connects the nail and magnet together. This force is applied by the magnet on the nail, and hence it’s called a magnetic force.

Here is one interesting question that I want you to answer; Is magnetic force is contact force, or in other words, is the contact between a magnet and nail necessary for the magnet to attract the nail?

When we move the magnet slowly towards the iron nail, and at this point, the nail also begins to move towards the magnet, it means the force came into action even when there was no contact between the magnet and nail. Hence, we can say that magnetic force is not a contact force.

What does this non-contact nature of magnetic force tell us

It tells us that there is an invisible field produced by the magnet in the space around it, and if you bring any ferromagnetic material in this field, then it experiences that force of attraction. We cannot see this field, but it exists.

Now one more interesting question, do you think that strength of this field is constant throughout the area around the magnet?

Let me explain it in easy way, suppose that there is a operating wireless fidelity router at some location. It provides us a signal altogether directions in some distance. currently so as to connect mobile to the net, we’d like to bring it to during this vary solely. This signal is stronger nearer the router.

“The nearer you bring your cellular phone to the router, the stronger the signal are”.

One can understand the magnet with same approach.  magnet contains a field of force around it. The strength of this field is bigger nearer to the magnet and reduces as we tend to go more far away from it.

As you bring any ferromagnetic object during this field, it experiences an attractive force. The nearer we tend to bring that object to the magnet, the larger the force it’ll expertise till at some purpose once the force are massive enough to create the item leap towards the magnet.

## Problems on magnetic field and magnetic force

Let us understand the relationship of magnetic field and magnetic force by solving some basic problems.

## Problem 1

Find magnetic field exerted on a charge of 20 coulomb is moving perpendicular to the direction of magnetic field with velocity 2m/s and experiences a force of 5 newton.

## Solution:

Given magnetic force,  $F_{m}$

Velocity of charge particle,  $v$

Magnetic field,

Strength of magnetic field is 0.125 Tesla.

## Problem 2

Find magnetic force experienced by a charge particle with 50coulomb charge moving with unit velocity at right angle to magnetic field of strength 2 tesla.

## Solution:

We know that equation of magnetic force and magnetic field is

So, force experienced by particle is 100 newtons.

## Q. How magnetic field and magnetic force varies with each other?

Ans: “The magnetic force F is directly proportional to the strength of magnetic field.” As magnetic field gets stronger, magnetic force also increase and vice versa.

## Q. At which point in magnetic field, the charge particle experiences strongest the magnetic force?

Ans: Magnetic field lines enter through south pole of magnet and leaves from north pole. Due to this magnetic force can be experienced strongest at either of the pole in comparison with opposite pole.

## Q. Does magnetic field affect magnetic force?

Ans: Force experienced by moving charge is different at different points in magnetic field.

Magnetic forces of attraction or repulsion caused by movement of electrically charged particles is responsible for electric motor and attraction of iron towards magnet like effects. Static charges experience electric field whereas electric field and magnetic field can be experiences among moving charges. This magnetic force among two moving charges can be understand as the effect on either charge by a magnetic field by other.

## Q. Why magnetic force is perpendicular to magnetic field?

Ans: If two objects or entities are at right angle with each other that means they are perpendicular to each other.

Because magnetic (Lorentz) field is directly proportional to $v\times B$, where v is velocity of moving charge and B is magnetic field strength. As we know, vector cross product is always at right angles to each other of the vector factors, the force is perpendicular to v.

## Q. Do magnetic force work?

Ans: Magnetic forces do not work.

For if Q moves an amount $dl= vdt$, the work done is

It happens because $(B\times v)$ is perpendicular to v, so $(B\times v).v= 0$

“Magnetic forces may reverse the direction in which charges particle moves but cannot speed it up or slow it down.”

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