Download magnetism and electromagnetism

MAGNETISM AND ELECTROMAGNETISM
1. MAGNETIC FORCES
A force is exerted on a charged particle by a magnetic field only when the particle
moves across the field lines. The force vector, F, is related to the cross product of the
velocity vector, v, and the magnetic field vector, B, as given by:
F = qv × B
The cross product is the component of velocity that is perpendicular to the field. If a
charged particle moves parallel to the magnetic field, the force exerted by the magnetic
field on the charged particle is zero. You can use the right hand rule to find the direction
of the force. Hold your thumb, forefinger and middle finger at right angles to each other. If
you point your forefinger in the direction of the velocity, and your middle finger in the
direction of the magnetic field, then your thumb points in the direction of the force.
When the motion of a charged particle moving with speed v is perpendicular to the
magnetic field lines, the magnitude of the force F is given by:
F = qvB
where q is the charge on the particle. If the charged particle is not moving perpendicular to
the magnetic field, but at some relative angle θ, the magnitude of the force is given by:
F = qvB sin θ
When a charged particle of mass m travels in a direction perpendicular to the magnetic
field, it moves in a circular path. The radius of the curved path r is given by:
r=
mv
qB
A current-carrying wire can experience a force when placed in a magnetic field. The
force is the strongest when the wire is perpendicular to the magnetic field lines. When the
wire is parallel to the field lines, there is no force. The magnitude of the force is given by:
F = IlB sin θ
where l is the length of the wire, I is the current flow in the wire and θ is the angle between
the current flow and the magnetic field.
2. MAGNETIC FIELDS
The electric current in a straight, current-carrying wire produces a magnetic field.
The direction of the magnetic field lines can be determined by the second right hand
rule. If you grasp the wire with your right hand, with your thumb pointing in the direction of
the current, your other fingers encircle the wire in the direction of the magnetic field. The
magnitude of the magnetic field at a distance r perpendicular to a wire carrying a current I
is given by:
KEY CONCEPT – MAGNETISM & ELECTROMAGNETISM
B=
µ0  I 
 
2π  r 
where µ0 is a constant known as the permeability of free space. This relationship holds
only so long as the length of the wire is much greater than the distance r.
Two parallel current-carrying wires exert a force on each other. For two parallel
wires carrying currents I1 and I2, and separated by a distance r, the force per unit length on
the wire carrying current I2, is given by:
F µ0  I1 I2 
=


l 2π  r 
The wires exert an attractive force on each other when their currents are in the same
direction. The wires exert a repulsive force on each other when their currents are in
opposite directions.
3. ELECTROMAGNETIC INDUCTION
Experiments by Michael Faraday in 1831 showed that although a steady magnetic
field produces no current in a coil of wire, a changing magnetic field can produce an
electric current. This phenomenon is known as electromagnetic induction. Faraday
determined that the induced emf is proportional to the rate of change of magnetic flux, φm,
passing through a flat loop of area, A, which is given by:
φ m = BAcos θ
where θ is the angle between B and a line perpendicular to the face of the loop. The unit of
flux is the weber (Wb). The induced emf is given by:
∆φ m
∆t
This is known as Faraday's law of induction. The unit of induced emf is the volt (V). The
minus sign in the equation relates to the direction of the induced emf. For a change in
magnetic flux through a coil of N loops, the induced emf is then given by:
ε=−
∆φ m
∆t
An induced emf always produces a current whose magnetic field opposes the original
change in magnetic flux. This is known as Lenz's law.
Another way to induce an electric field is by having a conductor move through a
uniform magnetic field B. A conducting rod of length, l, moving on a U-shaped conductor
with speed, v, perpendicular to a uniform magnetic field has an induced emf that is given
by:
ε = −N
ε = Blv
An electric generator is a device in which multiple loops of wires are forced to rotate in a
steady magnetic field. As the loops rotate, the magnetic flux through the loops varies as
the number of magnetic field lines through the loops varies from a maximum to zero.