Electromagnetism Notes

Electromagnetism

Learning Objectives

• Understand the concepts of electric charges and fields.

• Describe the behavior of magnetic fields, magnetic forces, and interactions between magnets and electric currents.

• Solve problems involving magnetic force exerted by the magnetic field.

Magnets

• Two of the same poles will repel, while opposite poles attract. This creates the magnetic force between two magnets.

• Certain materials, like those containing iron, can be magnets.

• Like poles repel; opposite poles attract.

• If a magnet is cut into two pieces, each piece will still have two poles.

• In magnets, like poles repel and opposite poles attract, just like electric charges. However, charges can be isolated, while magnetic poles cannot.

• Metals like cobalt, nickel, and iron are attracted to magnets, even if they are not magnets themselves.

Magnetic Fields

• Each magnet has its own magnetic field.

• A magnetic field can be represented with bar magnets, horseshoe magnets or electromagnetic fields.

Magnetic Field Lines

• Magnetic fields are made up of imaginary field lines, similar to electric fields. These lines describe the magnetic force in a given region.

• The field lines form a loop inside the magnet.

Compass

• A magnetic field is detected by its effect on a compass’ magnetic needle. The compass needle points to the North.

Earth's Magnetic Field

• Earth’s geographic poles are the axis of rotation of the planet.

• Magnetic poles exist due to the distribution of iron in the core.

• The positions of magnetic poles change due to changes in the position of iron and other magnetic materials in the core.

• Due to the large amount of magnetized material in the core, Earth’s magnetic field is immense, expanding into outer space.

Magnetic Domains

• Magnets are made up of tiny regions called magnetic domains, typically 1 square millimeter in area.

• Each domain has its own set of poles.

• The presence of a magnetic field in ferrous materials affects the domains, causing them to align with the field.

• In a material that is not magnetized, the magnetic domains point in random directions.

• In a magnetized material, all or most of the magnetic domains are arranged in the same direction.

Connection to Electricity and Magnetism

• An electric current produces a magnetic field.

• When current runs through an electric wire, the magnetic field it produces surrounds the wire.

First Right-Hand Rule

• The right-hand rule is used to determine the direction of the magnetic field around a current-carrying wire.

Formula of the Strength of Magnetic Field Near the Wire

$B = \frac{\mu_0 I}{2 \pi R}$

• $B$ = strength of magnetic field

• $\mu_0$ = permeability of free space, a constant ($1.257 \times 10^{-6}$ Tm/A)

• $I$ = current

• $R$ = distance away from the wire

Examples

1. ) How strong is the magnetic field of a wire that carries 4 A of current, 2 cm away from it?

2. ) How strong is the magnetic field of a wire that carries 4 A of current, 10 cm away from it?

Biot-Savart Law

• Biot-Savart Law defines the magnetic field produced at a point in space at some distance from a current-carrying conductor.

• The magnetic field is produced due to current flowing in the conductor.

• The Biot-Savart law was discovered by Jean Baptiste Biot together with Félix Savart.

• Biot-Savart Law states that “magnetic field due to a current-carrying conductor at a distance point is inversely proportional to the square of the distance between the conductor and point, and the magnetic field is directly proportional to the length of the conductor, current flowing in the conductor”.

Formula of the Strength of Magnetic Field Produced by a Moving Charge (Biot-Savart Law)

$B = \frac{\mu_0}{4 \pi} \frac{q v}{r^2}$

• $B$ = strength of magnetic field

• $\mu_0$ = permeability of free space, a constant ($1.257 \times 10^{-6}$ Tm/A)

• $q$ = magnitude of charge

• $v$ = velocity of charge

• $r$ = distance away from the wire

Examples

1. ) An 5 micro coulomb electron travels at the speed of 2200 km/s in a 180 degrees radius of 53m about the nucleus. Determine the strength of the magnetic field at the nucleus due to the motion of electron?

2. ) An 2 micro coulomb electron travels at the speed of 2200 km/s in a 50 degrees radius of 7 nm. Determine the strength of the magnetic field due to the motion of electron?

Formula of the Strength of Magnetic Field Produced by a Long Current Carrying Wire

$B = \frac{\mu_0 I}{2 \pi r}$

• $B$ = strength of magnetic field

• $\mu_0$ = permeability of free space, a constant ($1.257 \times 10^{-6}$ Tm/A)

• $I$ = current

• $r$ = distance away from the wire

Examples

1. ) Two 5-meter long parallel wires are separated 5 cm apart and carry 7A and 6A of current, respectively. Determine the magnetic field provided by a wire on the other wire.

2. ) A wooden chair is closed to a 10-meter long electric wire away by 4m and carries 10 A. Determine the magnetic field strength of the wire.

Try This!

1. ) How strong is the magnetic field of a wire that carries 5 A of current, AND 7m away from it?

2. ) A long straight wire carries a current of 5A. Calculate the strength of magnetic field at a distance of 0.1 m from the wire.

Formula of the Strength of Magnetic Field Across the Center of a Circular Coil with Loops

$B = \frac{\mu_0 I N}{2 r}$

• $B$ = strength of magnetic field

• $\mu_0$ = permeability of free space, a constant ($1.257 \times 10^{-6}$ Tm/A)

• $I$ = current

• $N$ = number of loops or turns

• $r$ = distance away from the wire

Examples

1. ) A thoroughly wound flat circular coil of wire has 125 turns and has a measured diameter of 15 cm that carries 5 A of current. Calculate the magnetic field at the center.

2. ) The magnetic field strength of a thoroughly wound flat circular coil of wire that has a measured diameter of 5 cm and carries 7 A of current is 7 mT. How many loops does the wire have?