Sunday, July 25, 2021

What is Ampere's circuital law | Physics class 12 notes

   


What is Ampere circuital law in physics?  ampere's circuital law and its application is most important topic of NCERT  Magnetic effect of electric current chapter   in Class 12.  Questions are frequently asked in the CBSE  board ,   ICSE Board and other competitive exam ( IIT JEE, NEET,  AIIMS, State Engineering exam )  from  Physics Chapter  .

“ampere's circuital law class 12 notes “ will be very beneficial for the students who are engaged in the preparation of  upcoming board exam and competitive exam .

In this  topic, the following terms will be illustrated.

Contents :

* 1. What is Ampere's circuital law

* 2. How to choose Amperian surface

* 3. Applications Of Ampere's Circuital Law

* 4. Magnetic Field Due To Carrying Current Straight Conductor

* 5. Solenoid

* 6. Electromagnet : Factors Affecting the Strength of an Electromagnet

* 7. Clock face rule , Ampere's right hand rule

* 8. Magnetic field due to a long current carrying solenoid

* 9. TOROID

* 10. Magnetic field B due to Ideal toroid

What is Ampere's circuital law :

The line integral of magnetic field B around any closed path is equal to μ0 times the total current enclosed by that path.


* This law is true for steady currents only.

* Ampere's circuital law can be used only for symmetrical current distribution.

How to choose Amperian surface

Choose Amperian surface such that

(i) Magnitude of Field B are same at every point on closed path

(ii) Angle between field and tangent must be same at every point on path

Or

(iii) Field B is perpendicular to tangent on close path

 

Applications Of Ampere's Circuital Law

 (i) Magnetic field due to a long straight conductor carrying current.

(ii) Magnetic field due to a solenoid carrying current.

(iii) Magnetic field due to current in a toroid.  etc

 

Magnetic Field Due To Carrying Current Straight Conductor

Consider a long straight conductor carrying current I  .


*  We have to find magnetic field B at a point P at a perpendicular distance r from the conductor.

Now Choose Amperian surface as a circular path of  radius r  such that

* The magnitude of B is the same everywhere on this closed path. And  the angle between B and dl is 0° everywhere on this path.

Apply  Ampere's circuital law to this closed path, we have,

 


                           Thus ,   


Solenoid

A coil having large number of close turns of insulated copper wire is called  solenoid .

* When an electric current is passed through the solenoid, it produces a magnetic field around it.

* The magnetic field produced by a current-carrying solenoid is similar to the magnetic field produced by a bar magnet.

* The magnetic field lines inside the solenoid are in the form of parallel straight lines. This indicates that the strength of magnetic field is the same at all the points inside the solenoid.

* One end of the current-carrying solenoid acts like a north-pole (N-pole) and the other end a south pole (S-pole). So, if a current-carrying solenoid is suspended freely, it will come to rest pointing in the north and south directions.

Electromagnet :

When a soft iron core is placed in Current carrying solenoid then system of solenoid and core is called  electromagnet.

* The core of an electromagnet must be of soft iron because soft iron loses all of its magnetism when current in the coil is switched off. On the other hand, if steel is used for making the core of an electromagnet, the steel does not lose all its magnetism when the current is stopped and it becomes a permanent magnet. This is why steel is not used for making electromagnets.

* Electromagnets can be made in different shapes and sizes depending on the purpose for which they are to be used.

Factors Affecting the Strength of an Electromagnet

The strength of an electromagnet depends on:

(i) The number of turns in the coil. If we increase the number of turns in the coil, the strength of electromagnet increases.

(ii) The current flowing in the coil. If the current in the coil is increased, the strength of electromagnet increases.

(iii) The length of air gap between its poles. If we reduce the length of air gap between the poles of an electromagnet, then its strength increases.

For example, the air gap between the poles of a straight, bar type electromagnet is quite large, so a bar type electromagnet is not very strong. On the other hand, the air gap between the poles of a U-shaped electromagnet is small, so it is a very strong electromagnet

Determine the polarity of electromagnet

1. Clock face rule


* If direction of current flowing in the coil looks anticlockwise from one end . Then that end  will be North pole (N-pole).

* If direction of current flowing in the coil looks clockwise from one end . Then that end  will be South pole (S-pole).

 

2. Ampere's right hand rule

Imagine to grasp the solenoid with right hand so that the fingers are curled in the direction of current. Then the thumb stretched parallel to the axis of the solenoid will point towards the N-pole end of the solenoid . 

 

MAGNETIC FIELD DUE TO A LONG CURRENT CARRYING SOLENOID

Magnetic field B inside a solenoid

Consider a long air- cored solenoid having closely packed coils


Let

 I = Current through the solenoid

N = number of turns in length L

 n = number of turns per unit length =  N/L

B = magnitude of magnetic field inside the solenoid

Now, Take Amperian  surface as a  rectangular closed  path abcd, where ab =  L

Apply  Ampère’s circuital law for closed  path abcda

Since the elemental lengths along bc and da are perpendicular to the magnetic field which is along the axis of the solenoid, then the integrals

Since the magnetic field outside the solenoid is zero, then the integral

 


Current Enclosed in Amperian loop = N I,     

Apply Amperes Circuital Law, We get 


Thus , Magnetic field inside  Long Solenoid is 

                       B = μ0 n I

It is Obvious that 

(i)  B depends only upon n and I.

(ii) It does not depend upon the "position within the solenoid. Therefore, magnetic field inside the solenoid is uniform.

   

MAGNETIC FIELD DUE TO A TOROID


TOROID :  

A solenoid bent into the form of a closed ring is called a toroid.

* The turns of a toroid are closely wound.

* The magnetic lines of force inside the toroid are circular and concentric with the centre of the toroid.

* Magnetic field B has a constant magnitude everywhere inside the toroid

* Magnetic field  is zero in the open space interior and exterior to the toroid.

(i) Magnetic field in the open space interior to the toroid is zero . If any closed path is inside the inner edge of the toroid, then there is no current enclosed. Therefore, by Ampere's circuital law, B = 0.

(ii) Magnetic field in the open space exterior to the toroid is zero. If any closed path is outside the outer edge of the toroid, each turn encloses equal and opposite currents so that net current enclosed is zero. Therefore, by Ampere's circuital law, B = 0.

Ideal Toroid :   A toroid that has closely wound circular turns

Real toroid :  In a practical toroid, the turns are in the form of spiral.

 

Magnetic field B due to Ideal toroid

* Consider an air-cored ideal toroid.

* The current flowing in the toroid sets up magnetic field of constant magnitude inside the toroid.

 Let

* I = current through the toroid

* r = mean radius of the toroid

* n = number of turns per unit length

* B = magnitude of magnetic field inside the toroid


In order to apply Ampere's circuital law, we choose the closed path (inside the turns) as a circle of radius r (dotted line path).

* Magnitude of B is the same everywhere on this closed path and angle between B and dl is zero everywhere on this path.

* Therefore, line integral of B over this closed path is given by ;

 

According to Ampere’s circuital law


Total current enclosed =  n x  length of path  x  I

I.e.    Ienclosed  =  n( 2πr ) I


so,      B ( 2
πr ) = μ0 n ( 2πr ) I

So,    B  = μ0 n  I 



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