FORM 6 PHYSICS: ELECTROMAGNETISM PART 2

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 AMPERE’S CIRCUITAL LAW

States that the line integral of magnetic field edu.uptymez.com   around any closed path in vacuum/air is equal to edu.uptymez.comtimes the total current (I) enclosed by that path
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I = current enclosed by that path.                                 

          Ampere’s  law is  an  alternative  to  Biot –  Savart law  but  it is  useful for  calculating  magnetic field  only in situations with considerable symmetry.

          This law is true for steady currents only.

           In order  to  use  law  it is  necessary  to  choose  a  path  for which it  is possible  to determine the  value of  the  line  integral

           It  is  because  there  are  many  situations where there  is  no such path  that  the law is of  limited use.

 Hence the application of ampere law
(i) Magnetic field due to constraining conductor carrying current
(ii)Magnetic field due to solenoid carrying current
(iii)Magnetic field due toroid

MAGNETIC FIELD DUE TO STRAIGHT   CONDUCTOR CARRYING CURRENT

 Consider a long straight conductor carrying current I in the direction as shown in the figure below

It is desired to find the magnetic field at a point p at a perpendicular distance r for the conductors

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Applying Ampere’s circuital law to this closed path
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 SOLENOID

Is a long coil of wire consisting of closely packed loops

Or

 Is a cylindrical coil having many numbers of turns 

         By  long  solenoid we  mean that  the  length of  the Solenoid is very large as  compared to  its  Diameter.

          Figure  below  shows the  magnetic field lines due to an  air cored solenoid carrying current

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  Inside the solenoid the magnetic field is uniform and parallel to the solenoid axis.

        Outside  solenoid  the  magnetic field is  very  small as  compared  to the  field inside  and  may be  assumed  zero.

        It  is  because the  same  no  of  field  line  that  are  concentrated  inside the  solenoid spread out  into very  faster  space  outside

Magnetic flux density due to an Axis of an in finely long Solenoid

 Consider  the  magnetic  flux  density edu.uptymez.com at P  due  to  a section of the  solenoid of  length  edu.uptymez.com

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 n = number of turns per unit length.

N= number  of  turns  the  section can be  treated  as a plane  circular coil of  N turns  in  which  case  dB is  given by

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Since dx is small, the section can be treated as a plane circular coil or N turns in which case dB is given by

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From the figure

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 Also

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Substituting for edu.uptymez.com and dx gives,

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The  flux  densities   at  P due to  every  section  of the  Solenoid  are  all  in the  same  direction  and  therefore  the  total  flux  density  B can  be  found by  letting  dB→o and  integrate over  the  whole  length of the  solenoid.

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The limits of integration are edu.uptymez.com and 0 because these values of β at the end of the solenoid.

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 If the Solenoid is Iron-cored of relatively permeability edu.uptymez.com magnitude of magnetic field inside the Solenoid is

                       From

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At points near the ends of an air cored Solenoid, the magnitude of magnetic field is

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The magnetic field outside a solenoid is zero

          Also in a current carrying long solenoid the magnetic field produced does not depend upon radius of the Solenoid.

TOROID
Toroid is a solenoid that bent into the form of the closed ring.
The magnitude field B has a constant magnitude every where inside the toroid while it is zero in the open space interior and exterior to the toroid.
If any closed path is inside the inner edge of the toroid then ther is no current enclosed. Therefore, by Ampere’s circular law B=0.

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Magnetic field edu.uptymez.com due to toroid
Consider the diagram below
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Let r = mean radius of toroid
I = Current through toroid
n = number of turns permit length
B = magnitude of magnetic field inside the toroid

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Thenedu.uptymez.com

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