Magnetic Force on a Current-Carrying Wire for JEE

VSAT 2022

What is a Force?

There are four fundamental forces of nature. The weak nuclear forces, the strong nuclear forces, the gravitational forces, and electromagnetic forces. Every force in this world will have the nature of one of the four fundamental forces. Every fundamental force originates in its own way. But, let us consider electromagnetic force for a moment. 


Electromagnetic force arises due to charged particles. These forces have two fields associated with themselves namely the electric field and the magnetic field. The electric field is responsible for electric force and is present even if the charged particle is not moving. The magnetic field is responsible for the generation of magnetic force but the field itself is only present when a charged particle is moving. In this article, we shall talk about magnetic force and its effect on a current-carrying wire.


Magnetic Force

When the electrically charged particles are moving, an attraction or repulsion will generate between them other than their electric interaction.  A charged particle can produce two fields, an electric field and a magnetic field. The magnetic field is generated only when the particle is in motion. This magnetic field is responsible for the generation of magnetic force. 


The magnetic force between two moving charges is the effect of the magnetic field created by one charge over another. Two particles containing charges moving in the same direction will be magnetically attracted toward each other and two charges with opposite directions of motion will magnetically repel each other.


Force on a Moving Charge in a Magnetic Field

Imagine a charged particle having charge $q$ moving with a velocity $v$ in presence of a magnetic field $B$. The magnetic force acting on the particle will be perpendicular to both velocity and magnetic field. 


Magnetic Force is formulated as:

${{\overrightarrow{F}}_{m}}=q\overrightarrow{v}\times \overrightarrow{B}$

The direction of magnetic force can be determined by Fleming’s right-hand rule.


As the magnetic force will always be perpendicular to the velocity, it will not change the magnitude but only the direction. Also, note that the work done by the magnetic force will be zero always. The direction of magnetic force can be determined by Fleming’s right-hand rule.


Magnetic Force on a Current-Carrying Wire

Imagine a wire carrying current placed inside a uniform magnetic field $B$. There will be a magnetic force on the wire due to the field. 


We have the formula for the magnitude of the magnetic force on a point charge.


$\left| \overset{\to }{\mathop{{{F}_{m}}}}\, \right|=\left| q\overset{\to }{\mathop{v}}\,\times \overset{\to }{\mathop{B}}\, \right|=qvB\sin \theta $


For a charge $q$ travelling length $L$ in a wire, it can be written as

${{F}_{m}}=q\frac{L}{t}B\sin \theta $, where $t$ is the time taken

${{F}_{m}}=\frac{q}{t}LB\sin \theta $

${{F}_{m}}=ILB\sin \theta $


The direction of magnetic force will be perpendicular to both the wire and the field. It can be predicted using the right-hand rule.


It makes the similar result for the wire as for point charge, i.e.,


$\overset{\to }{\mathop{{{F}_{m}}}}\,=\overset{\to }{\mathop{IL}}\,\times \overset{\to }{\mathop{B}}\,$


Applications of Magnetic Force

  • Electric motor: Magnetic force is the driving force for an electric motor. An electric motor converts electrical energy into physical movements. Electric motors generate magnetic fields when an electric current is passed. The magnetic field then causes a magnetic force with a magnet that causes movement or spinning that runs the motor.

  • Speakers: In order to convert an electromagnetic signal into sound, the speakers contain an electromagnet which is attracted and repelled from electromagnets and vibrates to produce the desired sound.

  • Compass:  A compass needle reacts to the earth’s magnetic field. The needle aligns itself with the earth’s magnetic field where it experiences the least magnetic force.

  • Microwave Ovens: Microwave Ovens also work with the help of magnetic force. A device named magnetron is used to power the Oven. It is a vacuum tube designed to circulate the electrons in a loop. A magnet is placed around the tube to provide the force needed to make the electrons circulate.


Conclusion 

When a charged particle moves in a magnetic field, It experiences a force in the direction perpendicular to the direction of motion. It is none other than magnetic force. Magnetic force does not contribute any energy to the charged particle as work done by the force is zero. However, the magnetic force has various applications. Small particles can be controlled by magnetic forces. It is applied in particle accelerators which are used in many important roles such as in nuclear reactors. It is also used in many everyday devices such as refrigerators, microwaves, speakers, and so on. Thus, the magnetic force is an important concept of Classical Physics.

FAQs on Magnetic Force on a Current-Carrying Wire for JEE

1. Can a stationary charged particle produce a magnetic field?

No, a stationary charged particle cannot produce a magnetic field. When a charged particle is at rest, it produces an electric field. But when a charged particle is in motion, it produces both electric and magnetic fields. The magnetic field is a property of moving charge only.

2. Define the expression for magnetic force on a point charge.

Imagine a charged particle having charge q moving with a velocity v in the presence of a magnetic field B. The magnetic force acting on the particle will be perpendicular to both velocity and magnetic field. 

Mathematically, the magnetic force $\overset{\to}{\mathop{{{F}_{m}}}}\,$ can be written as ${{\overrightarrow{F}}_{m}}=q\overrightarrow{v}\times \overrightarrow{B}$

3. What is the difference between the magnetic field and magnetic force?

A magnetic force is a force exerted by a magnet on another magnet or a piece of iron. A magnetic field gives the magnitude and direction of the magnetic force exerted on a magnet by another magnet or energised coil (one with current flowing through it). It is an example of a force field.


Weather reports often show a map with many arrows to show the strength and direction of the wind at all places on the map. This is another example of a force field and you could call it a wind field. The field is a cause, the force is an effect.

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