Showing posts with label Electromagnetism. Show all posts
Showing posts with label Electromagnetism. Show all posts

NEET 2025 Electro Magnetism Question on Magnetic moment of current carrying ciruclar coil

 

This video provides a step-by-step solution to a physics problem regarding the magnetic moment of current-carrying circular coils. Below is an SEO-friendly description written in simple English without special characters or symbols to help boost views for your video and blog.

NEET 2025 Physics Solution Magnetic Moment of a Circular Coil

In this video we solve a specific physics question from the NEET 2025 exam. The lesson focuses on the chapter of electromagnetism. We explain how to calculate the ratio of magnetic moments for two different circular copper coils when they carry the same amount of current.

What You Will Learn in This Video

This tutorial covers the fundamental formula for the magnetic moment of a circular conductor. You will see how the magnetic moment relates to the number of turns the current and the area of the coil. We break down the math simply so you can understand how changing the radius of a coil affects its magnetic properties.

Key Topics Covered

  • Understanding the magnetic field in a current carrying coil.

  • The formula for magnetic moment using current and area.

  • How to find the ratio of magnetic moments when radii are different.

  • Step by step calculation for a common entrance exam question.

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If you want more practice problems and detailed notes on electromagnetism please visit our blog. We have a full guide that explains these concepts in detail to help you prepare for your exams.

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Electromagnetism Complete Lesson

Electromagnetism is a branch of physics that deals with the magnetic field developed around the current carrying conductor or moving charge. To find the magnitude of the magnetic field induction, we can use Biot-Servert's law and ampere's law. We can define the fundamental unit to measure the current ampere basing on this definitions. We can also measure force between two straight conductors. As mentioned in the posts in the relevant topics, we can find magnetic induction for different kind of current carrying conductors using these rules.

If a current carrying conductor is placed under the magnetic field, it experience two magnetic fields and because of them, there is torque experienced by the current carrying conductor and we can design moving coil galvanometer basing on this concept. It can be even converted into Ammeter and voltmeter. All these are discussed in detail in the following posts.

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Magnetic Field Strength due to Current Problems and Solutions

We know that the magnetic field at the center of circular part due to straight line part of the conductor carrying conductor is zero. It is simply because the point is on the conductor itself.

We also know how to measure the field due to a circular part of the conductor and it is the total field itself. It is measured as shown in the above diagram.

We can also the find the direction of the magnetic field using the cork screw rule. Simply if the curled fingers indicates the direction of the current, the thumb indicates the direction of the magnetic field and that is inwards as shown.

Problem and solution

We need to find the magnetic field at the center of the circular arc part of the diagram where it is also has the current carrying conductor in straight shape.

The upper part of the straight conductor is at a distance equal to the radius of the arc and hence at the center of arc there will be magnetic field due to that straight conductor. According to the cark screw rule or thumb rule, the direction of the magnetic field is inwards.

The arc part also generates some magnetic induction and it can be measured as shown in the diagram below basing on the previous law. Its direction is outward.

The third part of the straight conductor will also generates some magnetic field induction and its direction is also outward.

To find the total magnetic field due to all of them, we shall add all the magnetic fields as shown in the diagram and with proper sign.



Problem and solution

We can solve one more problem basing on the same concept. We would like to measure the magnetic field at the center of the coil as shown below. We need to measure the field due to each part and we shall add all of them with proper sign to get the total magnetic field at the center.


Problem and solution

We need to find the magnetic field at the center of the coil that has infinite ladders as shown below. We just need to apply the formula that we have learned in the previous case and need to add all of them to get the total magnetic field as shown below.


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Magnetic field at a point due to different structures

A current carrying conductor will have magnetic field around it. It generates induction of certain magnitude and here we are interested in finding that at a certain point due to different structure.

We can use the combination of the Biot-servert’s law and ampere law to find the magnetic field at different points around a current carrying conductor.

For example, let us assume a finite straight conductor and we are interested in finding the magnetic field induction at a location that is in perpendicular to the current carrying conductor. Let us assume that the each end of the straight conductor is making some known angle at the point where we need to measure the field.

We can write the equation as shown below. We can extend this derivation to an infinite wire carrying current and it coincides with the derivation we have made in the previous case.


We can extend this discussion to a square shaped coil carrying current. The equation is same as the previous case. Any way the square is having four identical shapes and to find the total value of the magnetic field, we shall multiple the previous case value with four.

We can also do the same with a equilateral triangle shaped current carrying conductor. We need to find the magnetic field at the center of the triangle due to one part using the previous case and to get the total value of the magnetic induction, we shall multiply with three. All this is shown in the diagram below.



We can also find the magnetic field at a point due to current carrying conductor in the shape of a sector. Let us assume that we know the angle at the center and we can find the magnetic field at the center due to current carrying conductor as shown in the diagram below.

In the above diagram one more problem is solved. There we need to measure the magnetic field due to a current carrying conductor. It has a straight line part and also a circular part as shown in the diagram above.



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Torque acting on a rectangular coil

A rectangular coil can be placed between two strong poles of a magnet. If we pass current in that coil, around it in the perpendicular plane, a magnetic field is developed. Thus the coil is under the influence of two magnetic fields. Thus one pair of the sides of the coil experience a pair of forces acting in the opposite direction but at two different edges of the coil. That pair of forces generate a couple and turns the coil in a particular direction. Thus there is a torque developed in the coil and here we are interested in measuring it in the present lesson.

Let us consider a rectangular coil carrying current in it. Hence there is a magnetic field around it. Let us assume that it is placed between two poles of a magnet. We know that the current carrying conductor placed in a magnetic field experience a force. Thus each part of the rectangular coil experience a force. Any way this force in the horizontal sides of the coil is not going to produce any torque as it is acting along the length of the coil.


We can show the coil with current and the forces as shown below. If the coil is having number of turns, we shall count the force due to all turns by multiplying with the number of turns. The other two sides does not experience any force as the direction of the current and the magnetic field is same and hence the force due to magnetic field is zero.


The other two forces together constitute a couple and turns the coil. Thus a torque is developed and we can measure the torque as the product of any one force and the perpendicular distance between the two forces. We can measure it as shown in the diagram below.



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Force between two infinitely straight long conductors

Let us consider two infinitely straight long conductors carrying current in the same direction.We can measure the force between the two conductors as shown below. We need to use the formula that we have derived the formula for the magnetic field at a given point using the Ampere’s law.



Basing on the magnetic field, we have derived for the force experienced by the point at a distance using the formula that was also derived.

The second conductor also carrying current and experience due to the other conductor similar to the first conductor. These forces are mutual and we can derive as shown below.


Definition of ampere

We can  define  the ampere basing on the derivation as derived earlier. If two infinitely long straight conductors carrying a certain  current separated by  unit distance experience a force of repulsion per  unit length, the current passing through each conductor is one ampere.

This is treated like a fundamental unit in the SI system  and is defined  As shown below.




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Force on Current Carrying Conductor Fleming Left Hand Rule

We can find the magnetic field around a wire on the axial line of charge using the Biot-Servert’s law. We are not adding the derivation here and the expression is as shown in the figure.

Let us consider a point on the axial line at a particular distance and let us assume that we know the radius at any given point.



The expression for the magnetic field at any point can be expressed as shown in the diagram. If we are measuring it at the center of the circle, we need to equate the value to zero.


We can also find out the force acting basing on Biot-Servert’s law. We can find the magnetic field at any given point using this rule. We know that the magnetic induction is defined as the force experienced by a unit north pole when placed in a magnetic field.


Thus we can measure the force as the product of the pole strength and magnetic induction. As the field is small component, the force is also small component. To get the total force acting on the point, we need to integrate the given equation and we can get the total force as shown in the diagram below.


This force will be maximum when the point is perpendicular to the current carrying conductor. If  the angle is zero or 180 degree, the force will become zero as shown below.


To  find  the  direction of the force experienced  by  the current carrying conductor using Fleming Left hand rule. As per the law, if  fore finger  indicate the direction of the magnetic  field and central finger indicates  the direction  of the  current then the thumb  indicates the direction of the thrust or force experienced by the current carrying conductor.

We  can also measure the force acting on  a charge simply by defining  the current as the rate of charge. We can define as the cross product of velocity of the charge and the magnetic field and the product is multiplied  with the charge.


We can  define  the  unit of  magnetic  induction tesla basing  on the above derivation. The magnetic  field induction is the force experienced by the  conductor when a  unit charge passing through  a conductor with unit velocity  at right angle.



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Amepere's Law and Magnetic Field around Conductor

We can also find out the magnetic field induction at any point due to a charge using the Ampere’s law.According to this rule the line integral of magnetic induction around a closed curve is permittivity of free space times the current in that closed loop.


Problem and solution

Let us consider a current carrying conductor in circular shape and we are interested in the magnetic field at the center of the coil. We can use the formula that we have derived to do that and we shall assume that the distance of the particle on the perpendicular axis is zero. It is because we are measuring it at the center of the coil. The problem is solved as shown below.



When we measure the line integral, we get the length of the wire around which we are measuring the magnetic field. We also need to measure the magnetic field only due to currents inside the closed loop. We need not worry about the currents outside as they do not produce any impact. We are measuring only due to the portion of currents that are in the closed loop.

The currents with in the loop which are coming into the loop are treated as positive and currents leaving the closed circuit shall be treated as negative.



Basing on this Ampere’s law, we can find the magnetic field around a closed straight current carrying conductor of infinite length as shown below.

Let us assume a conductor carrying a current “I” as shown in the figure. We would like to measure the magnetic field around it at a distance “r” from it.  We can consider the line integral around it as the circular path of the given radius and when we line integrate it; we get the length of that closed path. It is nothing but the circumference of the circle.



It is the dot product of the magnetic field and the component of the length due to which we need to measure the field as per the Amper’s law. Any way the field and the portion of the length are in the same direction and the angle is treated as zero.

In the place of that line integral of the component of the length, we need to write the circumference as shown and we can find the magnetic field as shown below.



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Magnetic Field due to Current Carrying Conductor

In the beginning electricity and magnetism were treated like different subjects. People could not find any relation between them. Electricity is found to be due to the charges and magnetism is thought to be due to the different poles like north and south poles. The force between them and treatment of each subject is done quite separately and they do exist like to separate branches of physics.

In the earlier days of nineteenth century some experiments done by famous scientists found that with the change in the electric field, there is magnetic field also developed around it. This leads to new science called electromagnetism.

The experiments found that the charged particle in the state of rest gives electric field around it. If the charge is moving or if there is a flow of current in any conductor, around it there is not only electric field and there is also a magnetic field.

It can be noticed that the magnetic needle with north and south poles will keep on changing its direction around a electric charge as shown in the diagram.



We can find the direction of the magnetic field using different laws. One of those kinds of rule is Maxwell’s cork screw rule. If there is a nail that rotates using the right hand and if we rotate the screw in such a way that the nail advances in the direction of the current, the direction of the magnetic field is along the direction of the rotation of the head of the nail. It can be understood that the rotation of the head of the nail and the tip of the nail are in the perpendicular plane. Thus electric and magnetic fields are in the perpendicular plane.


We can also use a rule called right hand thumb rule to identify the direction of the magnetic field. It is somehow similar to cork screw rule. If we hold a current carrying conductor with our hand such that the thumb is along the direction of the current, the direction of the magnetic field is along the direction of the curled fingers. It again tells you that the electric field and the magnetic field are in the perpendicular planes.


Around every magnetic pole, there is some space up to where its influence can be experienced. That space is called magnetic field. If we keep any other magnetic pole with in that field, it experiences a force of attraction or repulsion. That force is called magnetic field induction. We can define the magnetic field induction as the force experienced by a unit North Pole placed in the magnetic field.

Around every current carrying conductor, there is a magnetic field and there is a magnetic field induction. To measure that value we have different rules and one among them is Biot-Servert’s law. According to this rule, the magnetic induction at any point directly proportional to the some factors like the  SIN angle it makes with the point, current passing in the conductor, component of the part of the length of the portion of the wire due to which we are measuring the magnetic field and is inversely proportional to the square of the distance of separation.




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Current Electricity Complete Lesson

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