# Magnetic Force And Mass: 3 Facts You Must Know

The intensity of the magnetic field depends upon the number of charges in motion, their velocity, and the field established in the surrounding.

Based on the magnetic field formula we can say that the magnetic force and mass are not related to each other, but you must be aware that the greater the configuration of the magnet more is the magnetic field set up covering the larger area.

## Is magnetic force mass?

The magnetic force in a field is stated by the formula F=qvBSinθ and if the velocity of the charges is perpendicular to the field then F=qvB

From this equation, we can see that the magnetic force is independent of the mass, but the magnetic field induced by the moving charges constitutes mass hence we can say that the magnetic field is due to the charged mass which produces the magnetic field and intensity.

Let us try to find out the magnetic field generated by the unit mass of a magnet. Consider a charged particle e moving in a helix path in a volume of dv. Let dl be the small element of a current carrying loop.

The magnetic field in a segment dl according to Biot – Savart’s Law is

The current flowing in a loop is

I=dq/dt

The total number of charges in the magnetic material is Ne

Hence, I=dq/dt(Ne-)

Using this in the above equation

The change in length segment per unit time is nothing but the velocity of the electron moving in a loop.

Now let us find out the density of the magnetic field per unit volume. The density of the magnetic field is the energy produced by the magnetic flux per unit volume.

It is given as

Which implies

For single electron N=1, hence,

Where

Now let us find the density of the magnetic mass which gives the energy per unit volume by the theory of relativity, since E=mc2, here energy E=um

The total volume of sphere is

Inserting the value of K now,

In relativity, the mass it equal to

Equating the both equations,

From this equation, we can calculate the magnetic field mass, and it relies upon the number density of the charges and the distance of separation from the source to the point.

## Does mass affect magnetic force?

The dimension of the magnetic field is given as F= M1T-2I^-1 which indicates that the magnetic force does depend upon the mass.

If the mass and configuration of the magnet are more, then it has a tendency to develop the magnetic flux covering the larger area as compared to the small magnets.

You can understand this by doing a simple experiment using the bar magnets, one of small length and pole size and another with a bigger in length, and introduce to it an area where you have spread the iron foils.

You will notice that for a small magnet, the iron foils from a nearby area get attracted but when you keep the bigger magnet in the same location, more magnets from far distance also get attracted towards the magnetic aligning the foils in magnetic lines.

Also for a larger mass, there are more charge carriers present within it to conduct the magnetic flux density and field, thus intensifying the magnetic effects.

## Does magnetism increase with mass?

The magnetism is directly proportional to the mass density of the material as we have discussed above.

The magnetic force is related to the angular velocity of the charged particle as these charges move in a helix in centripetal acceleration, and its velocity is inversely proportional to the charge that it carries.

Hence we can write the formula for the magnetic force and mass as

B=mω/q

Where B is a magnetic field,

m is the mass of the charged particle,

q is a charge, and

ω is an angular velocity of the particle.

## Are heavier magnets stronger?

The magnets are called to be strong magnets if they have the ability to form a magnetic field of higher strength and intensity.

The intensity of the magnetic flux depends upon the magnetic properties of the material used and the density of the flux penetrating through the material and the surrounding region, hence the stronger fields do not necessarily form by the heavier magnets.

If the density per unit volume of the magnet is more, then the accumulation of the charges within the magnet will be high. Hence, the magnetic flux density through the material of the magnet will be more, and hence the magnetic field strength will be stronger.

## What is the magnetic force produced by the electron moving in the magnetic field region of 1T with a velocity of 6.3*105 m/s?

Given:- v =6.3*105 m/s

B =1T

q =1.6*10-19C

The magnetic force is given by the equation

F=qvB

=1.6*10-19*6.3\*105*1

=10.08* 10-14N

The magnetic force produced by the electron is10.08* 10-14N.

## What is the magnetic field mass produced by the 3000 free electrons in the magnetized material at a point 0.2 fm away?

Given: e=1.6*10-19

N =3000

r =0.2 fm

The magnetic field mass is given by the formula

The constant

Inserting the values in this equation,

The magnetic field mass is found to be 3.84*10-26

## What is the magnetic field produced by the charge moving in a circular loop of radius 5cm having a mass of 7.3*10-23 moving with the velocity 3*104m/s?

r =5cm =0.05m

Since the charged particle is moving in a centripetal motion, the force acting on the charge is equal to

F=mv2/r

The force exerted on the charged particle is the magnetic force, hence we get,

Hence, we get the equation for magnetic field as

B=mv/qr

Inserting the values in this equation,

The magnetic field produced by the charged particle is 273.75 T.

#### Conclusion

The magnetic force depends upon the charge and the velocity of the charges in the field but it also depends upon the mass density and the magnetic field energy generated per unit volume by the moving charged particles.

AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn - linkedin.com/in/akshita-mapari-b38a68122