The Force On A Moving Charge In Magnetic Electric Field

When a moving charge interacts with a magnetic electric field, there are a lot of changes happening in moving charges and magnetic electric field. Before knowing the charges, we need to know that most of the magnetism is caused by the current, which means magnetism is caused by the flow of charge and magnetic fields apply some forces on the moving charges as they apply to the magnets. And the core concept is that wherever moving charge/charges are present, the magnetic field will apply forces on it/them. 

What happens to a moving charge in a magnetic field? 

Whenever a moving charge comes in a field that has the magnetic effect or is a magnetic field, it tries to move in a circular path, or the field forces the moving charge to follow a circular spiral path. A simple example of such force can be given by using the example of cosmic rays, where rays consist of charged particles, and when these particles interact with the earth, they get forced to move in a spiral field because of the magnetic force of the earth.  If the field is so strong, then the protons that are moving can be kept in a circular motion using the magnetic force. 

Using the right-hand rule, we can calculate the magnetic force on the moving charge applied by the magnetic fields. This force is pretty similar to the Coulomb force but affects both force and direction. The magnitude of magnetic force can be given by the following formula-

F = qvBsin

Where,

F = Magnetic force

q = Moving charge

v = Speed

B = Strength of magnetic field

= Angle between the direction of speed and field 

This force can also be referred to as Lorentz force, and using this force, we can define the strength of the magnetic field, and this calculation will be in terms of force applied to the moving charge in a magnetic field. According to the SI unit, we represent the strength of the magnetic field using Tesla. This unit is named after the inventor Nikola Tesla. 

Using the above formula magnetic field can be derived as

B = F/ qvsin

Unit Tesla can be given as follows- 

1 T = 1 N/C – (m/s) = 1 N/(A -m) 

How do moving charges interact with magnetic fields?

One thing that is very important to know is that the magnetic field conducts force directly on the charge. When it comes to classical electrodynamics, magnetic fields have the quality to not interact with each other. That means if any two electromagnetic fields pass by then, they will be undisturbed. Interaction between charges and magnetic fields can be determined using the right hand rule .

The direction of force applied by the magnetic field on the moving charge that is positively charged can be determined by placing the right hand in the direction of the field and the thumb in the direction of movement of charge. The direction of magnetic force will be perpendicular to the field and velocity. The fingers of the palm will represent the waves of field. If the charge is negatively charged, then the whole thing will be directly opposite. 

No magnetic forces will be generated on the static charges. The reason behind this is there is no magnetic field. The charge of static and electric fields by the charges will not affect the magnet, but while in motion, there will be a magnetic field generated by the charge, and that will apply a force on the magnet. Simply, we can say, if there is any relative motion between the magnetic field and charge then there will be no magnetic force on the charge.

Example 

To illustrate the above knowledge, we can take an example of a glass rod and silk component. After rubbing them together, we can place a charge on the rod. Let’s say the charge is 20-nC. After placing the charge, we throw the rod in the horizontal direction of the earth with 10m/s speed and magnetic force in the rod because the magnetic field of the earth needs to be calculated. 

Solution: First of all, we are required to know about the direction of the force that can be determined using the right hand rule. So as given above, the positively charged object has been thrown on the west side, and the field will be on the north side, and the force will be perpendicular to the field that is on the side of the earth’s core. 

Now, as discussed above,

B = F/ qvsin    

We know that = 90 so the sin90 = 1

Now 

F = (2010-9C)(10m/s)(510-5T)

     = 110-11N

Here we have calculated the magnitude of magnetic force as 110-11N.

Conclusion 

In the article, we have discussed the force on a moving charge in the magnetic electric field where we got to know that when a moving charge interacts with an external magnetic fields, there is force generated according to the right hand rule 1 perpendicular to the field and the magnitude of the force can be determined using the for formula B = F/ qvsin.