Download Today • Questions re: Magnetism problems 2 • HW: Magnetism

Magnetic Field due to Current
Today
• Questions re: Magnetism problems 2
• HW: Magnetism problems 2.5
• NEW concept: Magnetic field produced by an Electric Current
> Magnetic Field through a current loop
> Magnetic Field inside a Solenoid
• Magnetic Force between 2 parallel wires
Electromagnetism
April 22-26
Magnetic Field due to Current
April 22-26
Magnetic Field produced by a Current through a straight wire: When a
current I flows through a wire, there is a magnetic field B generated by that
current, such that
B = µ0I
2πR
where µ0 is called the "Permeability of Free Space", a constant whose defined
value is 4π E-7 T*m/A, and R is the "perpendicular distance" from the wire.
To find the direction of this magnetic field, we use a second
Right Hand Rule:
• Point your thumb in the direction of the current through the
wire;
• Curl your fingers "around the wire"; this circular direction is
the direction of the magnetic field.
A key idea here is that the magnetic field will completely circle around the
wire; the magnetic field "turns" in the directions that your fingers "curl".
• Note: the magnetic field is always such that, if you look at the wire as the
current comes TOWARDS YOU, the magnetic field will circle the wire
counter-clockwise.
Electromagnetism
Magnetic Field due to Current
April 22-26
Examples:
1.
A power wire carries a 10 A current to a microwave oven. What is the
strength of the magnetic field produced by this current a distance of 0.10
m from the wire?
2.
In a Physics lab, students powered small light bulbs with a 2.5 A current.
If a detector were placed a distance of 0.40 m from the wire, what is the
strength of the magnetic field due to this current? Note that the Earth's
magnetic field has a magnitude of 5 E-5 T; how does the magnetic field
due to the current compare to Earth's magnetic field?
3.
For the following diagrams, where the arrow indicates the direction of the
current, describe or draw the direction of the magnetic field.
⦿
Electromagnetism
Magnetic Field due to Current
April 22-26
Magnetic Field due to a Current in a wire loop: If a wire is formed into a
loop, when current flows through the loop, a magnetic field will be set up such
that the magnetic field will pass through the center of the loop.
In the diagram to the left, the magnetic field produced moves
through the loop from Left to Right; to determine the
direction of the magnetic field through a loop, we have, yes,
a third right-hand rule:
• Curl your fingers in the direction of the current through
the loop;
• Your thumb will tell the direction of the magnetic field
through the center of the loop.
This was a very important discovery; it showed physicists that they could take
a Circular magnetic field, where they could easily control its strength by
increasing or decreasing the current, and they could make that circular field
point in a specific direction (through the center of the loop).
Electromagnetism
Magnetic Field due to Current
April 22-26
Magnetic Field inside of a "Solenoid": A Solenoid is formed when a long
straight wire is formed into a series of loops, or a coil.
In the diagram to the left, the coil of wires
carries a current I as shown. Each individual
loop produces a magnetic field, and these are
S
N
in the same direction (through the loops).
These individual fields add together, giving
us an overall magnetic field that passes
through the solenoid.
To determine the direction of the magnetic field through a solenoid, you can
"wrap" or "curl" the fingers of your right hand in the direction that the current
flows through the coil, and your thumb will point in the direction of B.
To determine the strength (or magnitude) of the magnetic field inside the
solenoid, we use the following expression:
B = µ0IN = µ0In
L
where µ0 = 4π E-7, N represents the "number of loops" in the coil, L
represents the "length" of the Solenoid itself, and n is referred to as the "loop
density", or the "number of loops per unit length".
[E.g., if a Solenoid is constructed with N = 50 loops, and the length of the
solenoid is L = 0.10 m, then n = 50/0.10 = 500 loops per meter.]
Electromagnetism
Magnetic Field due to Current
April 22-26
Solenoid as Electromagnet: We describe a Solenoid as an "Electromagnet";
literally, a device that uses Electricity to produce or create Magnetism. By
running a current through the coil, we have a magnetic field that passes
through the center of the coil.
The diagram to the left compares an "Air
Core" solenoid to an "Iron Core" solenoid.
Of note is that, by filling the empty solenoid
with an iron core, the magnetic field strength
is increased (this is shown in the diagram
with magnetic field lines that are greater in
both number and density).
Also, notice in the equation for B that the Iron Core introduces a constant k
(this is referred to as the Relative Permeability); this is meant to imply that the
field strength will increase by some number that is associated with iron (for
Iron, k = 200). In essence, by filling the space with a magnetic material, you
effectively increase the strength of the Electromagnet.
Electromagnetism
Magnetic Field due to Current
April 22-26
Force between 2 parallel wires: When two wires, 1 and 2, carrying currents I1
and I2, are oriented parallel to one another, separated by a distance d, they will
exert a mutual force on one another such that we calculate the Force per unit
Length
FB = µ0I1I2
L
2πd
This force will either cause the wires to attract or repel each other.
⦿
⬇
⬆
In this configuration, where both wires carry currents in
the same direction, the force will be attractive. When
the currents are opposite, the force is repulsive.
×
d
⦿
⬇
I1
⬆
I2
×
This seemingly inconsequential concept is actually of vital importance in
Electricity; the definition of the unit of current (Ampere) is based on the force
between two parallel wires: When two parallel wires are separated by a
distance d = 1 m, there will be a mutually attractice force F = 2 E-7 N
when the wires carry a current of 1 Ampere.
Electromagnetism
Magnetic Field due to Current
Electromagnetism
April 22-26