Magnetism and Currents
Magnetism and Currents
In this section we learn that:
• A current generates a magnetic field.
• A magnetic field exerts a force on a current.
• Two contiguous conductors, carrying currents, will exert
forces on each other.
Magnetic Force on Current-Carrying Wire
• We saw that magnetic fields, exert forces on moving charges.
• But moving charges constitute a current
(either in vacuum or inside a conductor)
• Thus, a current-carrying wire will experience a force
when placed in a magnetic field
Magnetic Force on Current-Carrying Wire
If a segment of a wire of length L
carries a current I, in a region of
space where there is a magnetic
field B, then the wire experiences
a force F given by:
F  ILB sin 
Units( SI ) : N
The force is perpendicular to the current
according to the right hand rule:
point fingers in the direction of the current,
rotate or close towards magnetic filed, 
thumb points in the direction of the force
Magnetic Force on Current-Carrying Wire
A cooper rod 0.15 m in length, and 0.05 kg in mass,
is suspended from two thin, flexible wires,
in a magnetic field B = 0.550 T, as shown.
F  ILB sin 
Units( SI ) : N
Find:
a) The direction
b) The magnitude
of the current I needed to levitate the rod
Magnetic Forces on a Current Loop
A rectangular current loop
in a magnetic field
The force on each horizontal segment
is zero (I  B).
The force on each vertical segment
is F = I L B
The two forces are equal and opposite
 The loop is not displaced
However the forces exert a torque
on the loop
 The loop will rotate
Magnetic Forces on a Current Loop
The torque exerted by the magnetic force
on the loop is:
 w
 w

Ihb

 
2
2
  IBhw  IBA
  IhB 
In general, for an arbitrary
field-loop orientation:
  IAB sin 
Units( SI )N  m
For a loop with N turns and area A
  NIAB sin 
Torque on a Coil
A rectangular coil with 200 turns, is placed in a magnetic field B = 0.35 T.
If the maximum torque is 0.22 N m,
what is the current I on the coil?
Magnetic Field Produced by a Current
It was experimentally found that currents produce magnetic fields
For a straight long wire, that carries a current I, the lines of the magnetic field B
created by the current, are circles, centered at the wire, and perpendicular to it.
The direction of the magnetic field is given by the right hand rule, as shown above.
Magnetic Field Produced by a Current
Ampere’s Law is used to calculate the magnetic field
produced by a current (or current-carrying wire)
 B L   I
0 enclosed
Calculated along a closed path
0 = 4x10-7 T m / A = permeability of free space
B|| is the magnetic field parallel to the path
Magnetic Field Produced by a Current
Ampere’s Law
1.
2.
3.
4.
 B L   I
0 enclosed
Define the closed path
Divide the path in segments
Calculate B||L
Equate to 0 Ienclosed
For an infinite straight wire with current I
1.
2.
3.
4.
Path is circular loop with radius r
centered at wire and perpendicular to it
Segments are L all around the loop
B lines are circles around the loop
(empirical) so B|| = B all around, and
B||L = B 2r
Ienclosed = I  B 2r = 0 I
B
0 I
2 r
Magnetic Field Produced by a Current
For a long straight wire, that carries a current I, the lines of the magnetic field B
created by the current, are circles, centered at the wire, and perpendicular to it.
The direction of the magnetic field is given by the right hand rule, as shown below.
The magnitude of the magnetic field is:
0 I
B
2 r
The wire carries a current of 2.4 Amp. The particle has a charge of 52 C,
moves with a speed of 720 m/s and is at a distance of 13 cm from the wire.
Find the force on the particle
Force between two current-carrying wires
d
I1
I2
We know that a current I produces a
magnetic field B, at a distance r, given by:
We know that a current I, in a magnetic
field B, experiences a force F, given by:
0 I
B
2 r
F  ILB sin 
Calculate the force exerted on each other, by two parallel
conductors (length L, current I), separated by a distance d.
Is the force attractive or repulsive? What happens if one current is reversed?
Magnetic Field of a Current Loop
I
0 I
At the center of the loop:
B
For a loop with N turns:
N 0 I
B
2R
2R
Note that the magnetic field of a loop is similar
to the magnetic field of a magnet bar
Magnetic Forces Between Current Loops
If the currents are in the
same direction the two
loops attract each other
If the currents are in
opposite directions
the two loops repel
Magnetic Field of a Solenoid
A solenoid is a long wire
wound into a succession
of closely spaced loops
N
I
The magnetic field inside the solenoid is: B  0
L
Ideally, for a very long solenoid,
the magnetic field is zero outside the solenoid,
and parallel to the axis, and uniform in strength, inside.
Magnetic Field of a Solenoid
What would happen if
we place a magnet bar
near the solenoid?
A Solenoid
.. is a closely wound coil having n turns per unit length.
current flows
into plane
current flows
out of plane
What direction is the magnetic field?
A Solenoid
.. is a closely wound coil having n turns per unit length.
current flows
into plane
current flows
out of plane
A Solenoid
Consider longer and longer solenoids.
Fields get weaker and weaker outside.
Apply Ampere’s Law to the loop shown.
Is there a net enclosed current?
In what direction does the field point?
What is the magnetic field inside the solenoid?
current flows
into plane
current flows
out of plane
Apply Ampere’s Law to the loop shown.
Is there a net enclosed current?
In what direction does the field point?
What is the magnetic field inside the solenoid?
current flows
into plane
current flows
out of plane
B(L)  0 (nLI)

B  n 0 I
Magnetic Materials
The phenomenon of magnetism is due mainly to the
orbital motion of electrons inside materials, as well
as to the intrinsic magnetic moment of electrons (spin).
There are three types of magnetic behavior in bulk
matter:
Ferromagnetism
Paramagnetism
Diamagnetism
Remind me to ask you:
why does the magnet stick to the refrigerator?