Magnetism
The term magnetism comes from certain rocks called lodestones which contain iron ore, which is referred to as magnetite.
Magnets exert forces on one another. Like electric charges, magnets attract and repel one another and the strength of the forces exerted on each other depends on their distance from each other.
Each end of a magnet has a magnetic pole. Unlike electric charges, magnetic poles cannot be separated. If a magnet is broken in half, each new piece develops a north and south magnetic pole. The magnet will always have a north and south pole even if broken down to a single atom which suggests that atoms are magnets!
The space around the magnet contains a magnetic field. The direction of the field lines goes from the north to south pole.
A magnetic field is produced by the motion of electric charge. In a stationary magnet, electrons are moving constantly which produces electric charge. A spinning or orbiting electron produces additional magnetic fields so, every electron is a tiny magnet. Most substances are, however, not magnets because the various magnetic fields cancel each other out. In materials like iron, nickel, and cobalt, the fields do not cancel out entirely so, they can act like magnets.
The magnetic fields of individual iron atoms are so strong that iron atoms cluster up in alignment. These clusters are called magnetic domains. The difference between ordinary iron and an iron magnet is the alignment of domains. In common iron, the domains are randomly oriented but, if a strong magnet is introduced nearby, the domains orient in the direction of the magnetic field and the rotation of domains are brought into alignment. When an iron magnet is dropped or heated, the domains are jumbled out of alignment and causes the magnet to lose strength.
An electric current produces a magnetic field. A current carrying coil of wire with many loops is an electromagnet. Superconducting magnets are used in magnetic resonance imaging (MRI) in medicine and in "maglev" high speed trains.
A charged particle in motion experiences a deflecting force when it encounters a magnetic field. The force is greatest when the particle moves perpendicular to the magnetic field lines. The force becomes zero when it moves parallel to the magnetic field lines. Charged particles are deflected from outer space when they encounter the Earth's magnetic field which keeps the cosmic rays striking the surface of the Earth from becoming dangerous to life. If the direction of current in a wire is changed then, the deflecting force acts in the opposite direction. This principal has lead to the development of electric meters and electric motors.
The magnetic force on a point charge moving in a magnetic field (B) is:
F = qvBsin2
where F = force in Newtons; B = Tesla; v = velocity.
The force on a current carrying wire is
F = BILsin2
where L = length in meters
A current carrying loop of wire in a magnetic field experiences a torque
t = BIAsin2
The magnetic field produced by a current carrying wire is given by Ampere's Law
B = :oI/2Br
where :o = 4B x 10-7 T*m/A.
The magnetic force between two parallel conductors is
F = :oI1I2/2Bd
The magnetic field produced by a circular loop of wire carrying a current is
B = :oI/2R
The magnetic field inside a solenoid is
B = :onL
where n is the number of turns per unit length.
Review Questions:
1. A wire 0.50 m long carrying a current of 8.0 A is a right angles to a 0.40 T magnetic field. How strong is the force acting on the wire?
F = 1.6 N
2. A copper wire 40 cm long carries a current of 6.0 A and weighs 0.35 N. A certain magnetic field is strong enough to balance the force of gravity on the wire. What is the strength of the magnetic field?
B = 0.1 T
3. An electron passes through a magnetic field at right angles to the field at a velocity of 4.0 x 106 m/s. The strength of the magnetic field is 0.50 T. What is the magnitude of the force acting on the electron?
F = 3.2 x 10*-13 N
4. A stream of double charged anions moves at a velocity of 3.0 x 104 m/s perpendicular to a magnetic field of 9.0 x 10-2 T. What is the magnitude of the force acting on each ion?
F = 8.6 x 10*-16 N
5. A wire 0.50 m long carrying a current of 8.0 A is at right angles to a uniform magnetic field. The force on the wire is 0.40 N. What is the strength of the magnetic field?
B = 0.10 T
6. A wire 625 m long is in a 0.40 T magnetic field. A 1.8 N force acts on the wire. What is the current in the wire?
I = 7.2 mA or 7.2 x 10*-3 A
7. A proton is moving perpendicular to a magnetic field of 3 x 104 Gauss directed toward the top of this page. If the force on the proton is 2 x 10-11N and directed into the page, what is the (a) direction and (b) magnitude of its velocity?
a. Left b. v = 4.17 x 10*7 m/s
8. An electron is moving to the right side of the page with a velocity of 2 x 106 m/s directed 30 degrees with respect to the magnetic field of 4 T. Find (a) the direction and (b) the magnitude of the force on theelectron.
a. into the page.
b. F = 6.4 x 10*-13 N
9. Find the force of an electron (a) at rest in a magnetic field of 2T, and (b) moving at a velocity of 1 million, billion, trillion meters per second in the same direction as the magnetic field.
a. 0 because the charge has no velocity!
b. 0 because if the charge moves parallel with the field, it experiences no force!
10. A wire with a current of 15 A is positioned perpendicular to a magnetic field of 2 x 10-4 T. What is the magnitude and direction of the magnetic force on the wire if it is 2 meters long?
F = 6 x 10*-3 N into the page.
Honors:
11. A loop of wire is perpendicular to a magnetic field of 3 x 10-3 T. It carries a current of 3 A and has a radius of 100 cm. What happens to the loop?
torque = 0.0283 N*m
12. Calculate the magnetic field 10 cm perpendicular to the bisector of the line connecting two wires 2.0 cm apart and carrying antiparallel currents of 100 A each.
B = 4.0 x 10*-5 T
