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Charge in a Magnetic Field - Definitions, Concepts, and Formulas for JEE

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Last updated date: 12th Jul 2024
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What is a Magnetic Field?

A magnetic field is defined as a field in which moving electric charges, electric currents, and other magnetic materials can experience the magnetic influence. A moving charge present in the magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. In this article, we will study the concept of magnetic field due to moving charges and magnetism in detail.


What are Moving Charges?

A moving charge is an electric current that is circulating in any electric or magnetic substance, whether or not the charge is flowing through it. These moving charges or currents generate a magnetic field, which is denoted by $B$.


Force on a Moving Charge in a Magnetic Field

When a charge particle is moving, the magnetic field exerts the force on electric charge same as moving charge producing a magnetic field. With the increase in the magnetic field strength, the force will also increase. So, we can say that if charge has higher velocities, then the force will be larger.


A magnetic field experiences a force that is perpendicular to both its own velocity and to the magnetic field. 


Let an electric charge $+Q$ move with velocity v through the magnetic field $B$, then a force Fm is experienced by the electric charge. Now, consider a magnetic field that is acting along the $y-$axis, the charge moves along the $XY$ making angle  $\theta$ with the magnetic field. Now, we know that 

$ {{F}_{m}}\propto Q~v~B~\sin \theta  $ 

$ {{F}_{m}}=k~Q~v~B~\sin \theta  $ 


This force is also called the Lorentz magnetic force.


The cross product suggests that the force is always perpendicular to both the magnetic field and the velocity. As a result, it always acts out of the plane and will not contribute in charge's work. It can merely change the velocity's direction but will not change its magnitude. Fleming's Right-hand Rule makes it simple to establish the force's direction.


Fleming’s Right-hand Rule

According to Fleming's Right-Hand Rule, if we arrange our right hand's thumb, forefinger, and middle finger perpendicular to one another, the thumb will point in the direction of the magnetic force, the forefinger will point in the direction of the magnetic field, and the middle finger will point in the direction of the current.


A Brief on Lorentz Force

The force exerted on the charged particle $q$ moves with a velocity $v$ through an electric and magnetic field. This entire electromagnetic force $F$ on the charged particle is known as the Lorentz Force. This is given by the equation:

$\vec F=q~\vec E+q\left(~\vec{v}\times \vec B\right)$ 


Here, the first term is found by the electric field and the second term is the magnetic force which has a direction perpendicular to both the velocity and the magnetic field. The magnetic force exerted on a moving charge reveals the sign of the charge carriers present in the conductor. If the current is flowing from right to left in a conductor, the sign of the charge carriers is positive, and if the current is flowing from left to right, the sign of the charge carriers is negative.


How to Determine the Direction of Magnetic Force?

To determine the direction of the magnetic force on a moving charge, use the right-hand rule. Right Hand Rule state that to determine the direction of the magnetic force on a positive moving charge, point the thumb of your right hand in the direction of the velocity of the moving particle, the fingers in the direction of the magnetic field, and a perpendicular to the face of the palm points in the direction of Magnetic Force. The Magnetic Force is perpendicular to the plane formed by the velocity and magnetic field.


Right Hand Rule


Right Hand Rule


Magnetism

Magnetism is defined as the force which is exerted by the magnets when they attract or repel each other. Magnetism in a substance is generally caused by the motion of electric charges. This affected region around the moving charge consists of both an electric and magnetic field. A bar magnet is the most familiar example of magnetism which clearly gives us an overview of the concept, the bar magnet is attracted to a magnetic field and can attract or repel other magnets.

Magnetism can be classified into the following:

  • Diamagnetism

It is the tendency to be repelled by a magnetic field. Diamagnetism can be only observed in materials that contain no unpaired electrons. Examples of diamagnetic materials are gold, quartz, copper, etc.

  • Para magnetism

The magnetic moments align and thus are magnetised in the direction of the applied field. Examples of paramagnetic materials include lithium, molybdenum, etc.

  • Ferromagnetism

They can form permanent magnets and are also attracted to magnets. They have unpaired electrons and magnetic properties are experienced in a substance even after it is removed from the magnetic field. Examples of ferromagnetic materials include iron, cobalt, nickel, etc.


Causes of Magnetism

Magnetism is produced by the spin magnetic moment of elementary particles, such as electrons and the current travelling through the wire. Therefore, we can also say that magnetism is caused by the electromagnetic force present inside a substance.


Important Facts on Magnetism in Everyday Life

  • When a bar magnet is cut into two pieces along its length, the two pieces will behave like an independent magnet altogether, but the pole strength of the magnet will get reduced. 

  • A plane which passes through the geographic axis and is perpendicular to the surface of Earth (vertical plane) is called a geographic meridian.

  • The earth’s magnetic field varies from point to point in space. Does it change according to time? The Earth’s magnetic field does change with time. Although it takes a few hundred years to change by an appreciable amount, the variation in earth’s magnetic field with time cannot be neglected.


Conclusion

When a charge is moving in a magnetic field, it experiences a force which is perpendicular to both the velocity of the moving charge and the magnetic field. This force is given by the formula ${{F}_{m}}=QvB\sin \theta $. This force is also known as the Lorentz Magnetic Force. The direction of the force on a moving charge in the magnetic field is perpendicular to the plane formed by the velocity and magnetic field of the moving charge.

FAQs on Charge in a Magnetic Field - Definitions, Concepts, and Formulas for JEE

1. Is work done by magnetic field zero?

Yes, the direction of the magnetic force and velocity are always perpendicular to one another due to the way the magnetic force interacts with matter. The amount of work done will be zero if $\theta = 90$ because if force and velocity are perpendicular, then force and displacement are also perpendicular. Thus, work done by the magnetic force is always zero and the kinetic energy of the charge remains unchanged. 

2. What is a magnetic field?

A magnetic field is defined as a field in which moving electric charges, electric currents, and other magnetic materials can experience the magnetic influence. The magnetic fields are produced by the moving electric charges and the intrinsic magnetic moments of elementary particles associated with their spin.

3. What is meant by Lorentz force?

When a moving charge passes through both the electric and magnetic fields, the net force experienced by the moving charge is known as Lorentz force. It is basically the sum of the magnetic and electric forces.