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NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law

NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law

Ampere’s Circuital Law

According to Ampere’s circuital law, the line integral of the magnetic field B around any closed path is equal to NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 1 times the net current I threading through the area enclosed by the closed path. Mathematically,
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 2
Now, consider the diagram below
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 3
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 4

Applications of Ampere’s law

The followings are the few important applications of Ampere’s law may be given as

  •  Magnetic field due to Straight Current Carrying Wire

The magnetic field due to a current carrying wire of finite length at a point P situated at a normal distance r is From Ampere’s law,
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 5

NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 6
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 7
When point P lies on axial position of current carrying conductor, then magnetic field at P, B = 0

  •  Magnetic Field due to a Thick (Cylindrical) Wire

Let us have a thick cylindrical wire of radius R and infinite length, which carries a current I. Then,
magnetic field at a point outside the wire NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 8 where, r is the distance of given point from centre of wire and r> R.
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 9
Magnetic field at a point inside the wire at a distance r from centre of wire (r < R) is
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 10
Magnetic field inside a hollow current carrying conductor is zero.

  •  Magnetic Field due to a Solenoid

NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 11
A current carrying solenoid behaves as a bar magnet. The face, where current is flowing clockwise behaves as South pole and the face, where current is seen flowing anti-clockwise, behaves as North pole.
For such a solenoid, the magnetic field inside it is uniform and directed axially.
For a solenoid coil of infinite length at a point on its axial line, the magnetic field
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 12
where, n is number of turns per unit length.
At the end of solenoid NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 13
At the end field is half of at the centre this is called end effect.

  •  Toroidal Solenoids

For a toroid (i.e. a ring shaped closed solenoid) magnetic field at any point within the core of toroid
NEET Physics Notes Magnetic Effects of Current-Ampere’s Circuital Law 14

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