Transcript Using the “Clicker”

The force on a current-carrying wire
A magnetic field exerts a force on a single moving charge, so
it's not surprising that it exerts a force on a current-carrying
wire, seeing as a current is a set of moving charges.
F  qvB sin 
Using q = I t, this becomes: F  IvtB sin 
But a velocity multiplied by a time is a length L, so this can be
written:
F  ILB sin 
The direction of the force is given by the right-hand rule, where
your fingers point in the direction of the current. Current is
defined to be the direction of flow of positive charges, so your
right hand always gives the correct direction.
Three wires
Consider three wires carrying identical currents between
two points, a and b.
The wires are exposed to a uniform magnetic field.
Wire 1 goes directly from a to b. Wire 2 consists of two
straight sections, one parallel to the magnetic field and
one perpendicular to the field. Wire 3 takes a meandering
path from a to b. Which wire experiences more force?
1. Wire 1
2. Wire 2
3. Wire 3
4. equal for all three
Three wires
The force is equal for all three. What matters is the
displacement perpendicular to the field, and that's equal for
all wires carrying equal currents between the same two points
in a uniform magnetic field.
The force on a current-carrying loop
A wire loop carries a clockwise current in a uniform
magnetic field directed into the page. In what
direction is the net force on the loop?
1. Left
2. Right
3. Up
4. Down
5. Into the page
6. Out of the page
7. The net force is zero
The force on a current-carrying loop
The net force is always zero on a current-carrying loop in a
UNIFORM magnetic field.
Is there a net anything on the loop?
Let’s change the direction of the uniform magnetic field. Is the
net force on the loop still zero? Is there a net anything on the
loop?
Is there a net anything on the loop?
Let’s change the direction of the uniform magnetic field. Is the
net force on the loop still zero? Is there a net anything on the
loop?
The net force is still zero, but there is a net torque that tends
to make the loop spin.
The torque on a current loop
The magnetic field is in the plane of the loop and parallel to
two sides. If the loop has a width a, a height b, and a current
I, then the force on each of the left and right sides is F = IbB.
The other sides experience no force because the field is
parallel to the current in those sides. Simulation
The torque (   rF sin  ) about an axis running through
the center of the loop is:
a
a
  F F
2
2
 aF
 IabB
The torque on a current loop
  IabB
ab is the area of the loop, so the torque here is   IAB .
This is the maximum possible torque, when the field is in the
plane of the loop. When the field is perpendicular to the loop
the torque is zero. In general, the torque is given by:
  IAB sin 
where  is the angle
between the area
vector, A, (which is
perpendicular to the
plane of the loop) and
the magnetic field, B.
A DC motor
A direct current (DC) motor is one application of the torque
exerted on a current loop by a magnetic field. The motor
converts electrical energy into mechanical energy.
If the current always went the same way around the loop, the
torque would be clockwise for half a revolution and counterclockwise during the other half. To keep the torque (and the
rotation) going the same way, a DC motor usually has a "splitring commutator" that reverses the current every half rotation.
Simulation
The force between two wires
A long-straight wire carries current out of the page. A
second wire, to the right of the first, carries current
into the page. In which direction is the force that the
second wire feels because of the first wire?
1. Left
2. Right
3. Up
4. Down
5. Into the page
6. Out of the page
7. The net force is zero
The force between two wires
In this situation, opposites repel and likes attract!
Parallel currents going the same direction attract.
If they are in opposite directions they repel.
A loop and a wire
A loop with a clockwise current is placed below a long
straight wire carrying a current to the right. In which
direction is the net force exerted by the wire on the
loop?
1. Left
2. Right
3. Up
4. Down
5. Into the page
6. Out of the page
7. The net force is zero
A loop and a wire
The long straight wire creates a non-uniform magnetic field,
pictured below.
A loop and a wire
The forces on the left and right sides cancel, but the forces on
the top and bottom only partly cancel – the net force is
directed up, toward the long straight wire.
The field from a solenoid
A solenoid is simply a coil of wire with a current going through
it. It's basically a bunch of loops stacked up. Inside the coil,
the field is very uniform (not to mention essentially identical to
the field from a bar magnet).
For a solenoid of length L, current I, and total number of turns
N, the magnetic field inside the solenoid is given by:
B
0 NI
L
The field from a solenoid
B
0 NI
L
We can make this simpler by using n = N/L as the number of
turns per unit length, to get: B  0 nI .
The magnetic field is almost uniform - the solenoid is the
magnetic equivalent of the parallel-plate capacitor. If we put a
piece of ferromagnetic material (like iron or steel) inside the
solenoid, we can magnify the magnetic field by a large factor
(like 1000 or so).
Magnetism on the atomic level
Currents in wires produce magnetic fields. What produces the
magnetic field from a bar magnet, where there are no wires?
Why does that field look like the field of a solenoid?
Consider the Bohr model of the atom, where electrons travel
in circular orbits around the nucleus. An electron in a circular
orbit looks like a current loop, so it produces a magnetic field.
In some materials (ferromagnetic materials) the magnetic
moments associated with the atoms align, leading to a large
net magnetic field.
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