Download chapter – 5 magnetic effects of electric current and

CHAPTER – 5
MAGNETIC EFFECTS OF ELECTRIC CURRENT
AND MAGNETISM
SYNOPSIS :
•
Electrodynamics :
The branch of physics which envelops a comprehensive study of
electricity and magnetism (now known as electromagnetism) is
called electrodynamics.
•
Oersted’s observation :
Magnetic field is produced around a conducting wire carrying
electric current.
•
Biot - Savart’s Law :
The intensity of magnetic field due to electric current element
→
→
I dl at a point having a position vector r with respect to electric
→
→ ∧
μ0 I dl × r
current element is given by formula dB =
4π r 2
•
Direction of magnetic field due to a straight conductor
carrying electric current :
If a straight conducting wire carrying current is held in right hand
such that thumb is in the direction of electric current the fingers
encircling the wire indicate the direction of magnetic field lines.
•
Direction of magnetic field at any point on the axis of
circular ring carrying current :
To find the direction of magnetic field on the axis of the ring curl
the fingers of right hand in the direction of flow of electric current.
The thumb stretching perpendicularly to the plane of the circle
formed by the fingers indicates the direction of magnetic field.
•
Solenoid :
A helical coil consisting of closely wound turns of insulated
conducting of closely wound turns of insulated conducting wire is
called a solenoid.
• Magnetic field obtained due tosolenoid electrically charged :
For a very long solenoid (in principle of infinite length) magnetic
field in uniform inside the solenoid and its direction is parallel to
the axis of the solenoid, while the magnetic field outside the
solenoid is zero.
• Ampere’s Circuital law :
“The line integral of magnetic induction over a closed loop in a
magnetic field is equal to the product of algebraic sum of electric
currents enclosed by the loop and magnetic permeability.”
→→
v∫ B ⋅ dl
= μ 0 ΣI
• Third pillar of Maxwel’s electromagnetic theory is the fact that
magnetic field lines form closed loops.
• Toroid :
If a solenoid is bent in the form a circle and its two ends are
connected to each other, then the device is called a toroid.
OR
A device prepared by closely winding an insulated conducting wire
around a non-conducting hollow ring is called a toroid.
• In such a toroid magnetic field in the central region and outside
the toroid is zero.
• Toroid is a very useful component of Tokamak used for nuclear
fusion for infinite source of energy.
• Ampere’s observation :
The parallel wires placed near each other exert a force of
attractive if they are carrying currents in the same direction and a
repulsive force, if they are carrying currents in the opposite
direction.
• Ampere :
When the magnetic force acting per meter length in two infinity
long wires placed parallel to each other at a distance of 1 meter in
vacuum carrying identical currents is 2 × 10-7 N, the current
passing through each wire is 1 ampere.
• Coulomb :
When a steady electric current passing through a conductor is 1
A, the quantity of charge passing through a cross section in one
second is called 1 coulomb.
• Lorentz force :
→
If q electric charge is passing through the magnetic field B and
→
→
electric field with intensity E with velocity Vd , then magnetic
⎛→⎞
⎛→⎞
⎝
⎝
field ⎜ Fm ⎟ and electric field ⎜ Fe ⎟ act on the electric charge and in
⎠
those
⎠
circumstances this electric charge moves under total force
→
two forces. The total force F acting on this electric
of these
charge.
→
→
→
F = Fe (electric force) + Fm (magnetic field)
→
⎛ → →⎞
= q E + q ⎜ υd × B ⎟
⎝
⎠
⎡→
⎛ → → ⎞⎤
⎣
⎝
= q ⎢ E + q ⎜ υd × B ⎟ ⎥
⎠⎦
The force given by this equation is called Lorentz force.
• Cyclotron :
A cyclotron is a machine used to accelerate charged particles. In
this machine, electric charges are accelerated by using electric
and magnetic fields.
Principle :
On increasing momentum of the charged particle entering
perpendicularly, the uniform magnetic field, the radius of its
circular path increases, but there is no change in its frequency.
• Principle of moving and pivoted coil galvanometer :
A current carrying coil suspended in a uniform magnetic field
experiences a torque and gets deflected.
• The magnitude of the magnetic force depends on the velocity of
the particle, hence such a force is called velocity dependent force.
• The ratio
e
is a constant called the gyro-magnetic ratio and its
2m
value is 8.8 × 1010 C kg-1.