# Moving Charge and Magnetism Explanation with Handwritten Notes

So we all love playing with magnets, the way they get to cling to a metal object and repel when the same side of two magnets are brought close to each other. Well in this article, I will be telling you about moving charges which is the actual reason for this whole magnetism and will give you all the details regarding magnetism for class 12th board.

My personal handwritten notes with all the derivation of this chapter 4 moving charge and magnetism from class 12th physics.

## Magnetic field

So we know about what an electric charge and electric field is, if you don't know click here this link will redirect you to our article where we have taught about electric charge and field.

So we have learned that the electric field is created by a charge, known as source charge Q. This electric field is the area around source charge where the effect can be experienced. Now if you put another test charge q in an electric field, it will experience some force in some direction depending upon the charge present on source charge and test charge is positive or negative.

In this electric and magnetic field, both fields are mostly the same, but the electric field is created because of static charges whereas the magnetic field is created due to moving charge.

So you can also say, the electric field is created due to stationary charge and the magnetic field is created due to moving charge or current.

Both of these fields are almost the same in property, therefore both these fields also obey the principle of superposition.

### Lorentz force:

Both of us know that when a test charge is moving it creates a magnetic field. Now imagine a moving charge present in both an electric field and a magnetic field. Some force is applied by both magnetic and electric fields on this charge.

This force is given by the Lorentz force.

We already know about force created due to the electric field, but in case of electric force, one thing you will notice is that we are dealing with the electric charge at the static position but a magnetic field is created due to moving electric charge and therefore here the charge is not a static state and moving continuously.

Due to this movement of electric charge, the force due to the magnetic field at a given spot depends on time as well.

So according to Lorentz force, imagine an electric charge 'q' moving with the velocity 'v' and at any particular time 't' this charge is present at some position 'r'.

Now at the particular moment of time 't' when the charge is at position 'r'. The force on the charge due to the electric field will be E(r) and force due to the magnetic field will be B(r).

So, therefore, net force on this charge 'q' will be:

F=q[E(r) + v * B(r)] = Felectric + Fmagnetic

So total force on charge q will be the combined force due to electric and magnetic field.

P.s: Magnetic field is created due to the movement of charge at velocity 'v' therefore to find force due to the magnetic field we have multiplied it with 'v' but the electric field is created due to static charge so therefore we have not multiplied it with 'v'.

### Motion in the magnetic field:

Now let's see what will be the movement of charge when it's in the magnetic field?  We will see, in what direction will it move? How will it move?

We will see two different cases, 1. When the charge is moving in the direction of the magnetic field and 2. When the charge is entering a magnetic field with some angle.

Case 1: When the direction of charge entering the magnetic field and the direction of a magnetic field is the same. The angle (θ) between the direction of moving charge and a magnetic field is 0.

Force (F) in the magnetic field is F= qVB.sinθ. Since here θ = 0, we know that sin θ= sin 0 = 0.

So therefore in case 1, there is no force and effect when electric charge enters into the magnetic field.

Case 2: When electric charge enters a magnetic field with some angle θ. To find the effect of the magnetic field on an electric charge. We need to see the effect of two components of electric charge when it enters the magnetic field. Image credit: Examfear.com

As you can see in the diagram, component Ucosθ is along the direction of the magnetic hence parallel to the magnetic. Due to this component U.cosθ, there will be no force acting on electric charge and it will keep on drifting along the magnetic field.

Due to component U.sinθ which is parallel (丄) to the magnetic field (B), it will be turned.

Due to these components, U.sinθ and U.cosθ, the charge will move in helical motion when entering into a magnetic field.

So the conclusion is when charge enters into a magnetic field and angle (θ) between the direction of the magnetic field and charge entering a magnetic field is zero. Then there will be no force acting on an electric charge.

If charge enters into a magnetic field with some angle, then the charge will move in helical motion inside a magnetic field.

### Motion in a combined electric and magnetic field:

Now we have seen, what will be the moment of electric charge when it enters the magnetic field, but one thing of you will not think of is, electric charges creates an electric field and when an electric charge is in a magnetic field.

So electric charge is actually moving in both electric as well as magnetic field. We have only seen what will happen if electric charge enters a magnetic field, but will have electric field present in the magnetic field have some other kind of effect?

What will be the motion of electric charge in a combined electric and magnetic fields? Let's see.

So, from Lorentz force we know that:

Force on a charge moving with charge 'q' with velocity 'v' where both electric and magnetic field are present will be

F=q[E(r) + v * B(r)] = Felectric + Fmagnetic

Here, we will use vector notation to find the direction in which charge will be moving due to the effect of an electric and magnetic field.

We shall consider that electric, magnetic field and velocity of particle all three of them are perpendicular to each other as shown in the image.

So, therefore, using vector notation: Electric field (E) = E.j , Magnetic field (B) = B.k , v=v.i.

P.s: Here 'j', 'k' and 'i' are a unit vector of their respective axis.

So, therefore:

Force due to electric field (FE) = q.E= qE.j ;

Force due to magnetic field (FB)=qv*B=q(v.i * B.k) = -q.vB.j

and net electric force will be on charge q is F= q(E-vB)

P.s: Here 'j' vector notation shows that direction in which force will effect.

## Bio-savart's law:

So as we know that the magnetic field is created due to current or moving electric charge. So because current creates a magnetic field, therefore there should be some relation between a current and magnetic field.

This relation between current and magnetic field is given by Bio-savart's law

As you can see in the above image, this is the image of the conductor with current 'I' and due to this current in a conductor.

Let's suppose a small length (infinitely small length) of this conductor be 'dl' therefore 'dB' will be the magnetic field at point 'P' due to this element 'dl' with current 'I'.

So bio-savart's law states that: This magnetic field 'dB" is directly proportional to the amount of current 'I' and element 'dl' but it will be inversely proportional to the square of distance 'r' between element 'dl' and point 'P'.

Derivation of Bio-Savart's law and all the other details are provided in our notes of this chapter 4 moving charge and magnetism.

## Handwritten notes:

This article is a brief summary of chapter 4, Moving Charge and Magnetism for all the derivation related to this chapter and other important things. I have prepared my special handwritten notes. These notes have all the derivation of this chapter.