Magnetic effects of current and magnetism-I : By R.Buvana Magnetic effects of current and magnetism-I
Concept of Magnetic Field : Concept of Magnetic Field The space around a current carrying conductor , in which its magnetic effect can be experienced , is called Magnetic Field (B).The electric and magnetic fields differ from each other on the following accounts 1.whereas the source of electric field is electric charge the source of magnetic field is current element 2.whreas the lines of electric field due to a charge distribution start from one point and end at some other point, the lines of magnetic field due to a current element start and end at the same point i.e. they form closed loops.
Magnetic lines of force : Magnetic lines of force The magnetic field strength at any point in a magnetic field may be defined as a vector quantity, whose magnitude is equal to number of magnetic lines of force passing per unit small area around that point and whose direction is along the tangent drawn at that point on the magnetic line of force.
Biot-Savart Law : Biot-Savart Law According to Biot- Savart the magnetic field produced due to this current element at a point p distant r from the element is
1.directly proportional to the current flowing in the element
2.directly proportional to the length of element
3.directly proportional to sin?,where ? is the angle between current element and the line joining current element to point P.
4. inversely proportional to the square of the distance of the element from point p
B=µ0/4p I dl sin ?/r²
Conti… : Conti… 10¯7=µ0/4p Weber/ampere-meter
Unit of Magnetic field- In S.I system, the unit of magnetic field is tesla or Weber/m²
The CGS unit of magnetic field is Gauss.1 G=10¯4 tesla.
The direction of magnetic field due to a current carrying conductor can be found by applying the right hand thumb rule and Maxwell cork screw rule. According to Right hand thumb rule if we grasp the conductor , in the palm of the right hand so that the thumb points in the direction of the flow of current, then the direction in which the fingers curl, gives the direction of magnetic field lines.
Magnetic field due to an infinitely long current carrying straight wire. : Magnetic field due to an infinitely long current carrying straight wire. B=µ0/4p 2I/R
Magnetic field due to a current carrying circular loop : Magnetic field due to a current carrying circular loop B=µ0/4p 2pIn/R at center
B=µ0/4p 2pIn/(R²+x²)³/² at axis
Ampere’s Circuital law : Ampere’s Circuital law The line integral of magnetic field induction along the boundary of a closed path is equal to µ times the net current enclosed by the path.
?B.dl=µ0I
Applications of Ampere’s Law : Applications of Ampere’s Law 1.Magnetic field due to a current carrying infinitely long straight wire
B=µ0/4p 2I/R
2.Magnetic field due to a straight current carrying long solenoid
B=µ0nI
3.Magnetic field due to Toroidal Solenoid
B=µ0nI
Homework questions : Homework questions 1.The magnitude of the magnetic field 80.0cm from the axis of a long straight infinite wire is 7.0 µT. Calculate the current in the wire. (28A)
2.A circular coil of wire of 50 turns, each of radius 0.08 m carries a current of 0.8A.Find the magnetic flux density at the centre of the coil. (3.1 x10??4T)