The Earth’s Magnetic Field

Subject: 

PHYSICS

[mediator_tech]

Term:

FIRST TERM

Week:

WEEK 6

Class:

SS 3

Topic:

The Earth’s Magnetic Field

When a magnetic needle or a bar magnet is freely suspended, it comes to rest roughly in the N-S

poles of the earth. This shows that the earth acts like a magnet, hence, the earth must have N-S Poles near the geographical poles.

The angle between the magnetic North and the geographical North directions at a place is called “the angle of Declination or Variation”

The earth’s magnetic field

The Angle of Dip

This is the angle between the horizontal and the resultant earth’s magnetic field. It can also defined as the angle between the total intensity of the earth’s magnetic field and the horizontal.

However, the angle of dip, declination and the earth’s horizontal field strength are called magnetic element.

EVALUATION

1. Distinguish between angle of dip and angle of declination.

The angle of dip and the angle of declination are two different aspects of the earth’s magnetic field. The angle of dip is defined as the angle between the horizontal and the resultant earth’s magnetic field, while the angle of declination is defined as the angle between total intensity of the earth’s magnetic field and the horizontal. Additionally, other important magnetic elements include the strength of the earth’s horizontal field and other parameters such as inclination and intensity. Overall, these different aspects of the earth’s magnetic field play an important role in our understanding of the planet’s overall dynamics and behavior.

Enumerate the magnetic elements.

The magnetic elements of the earth’s magnetic field include the angle of dip, the angle of declination, the strength of the horizontal field, and other parameters such as inclination and intensity. These different aspects of the earth’s magnetic field are important for our understanding of how the planet interacts with its environment and responds to external forces such as solar radiation and geologic activity. Additionally, variations in these elements over time provide valuable insights into the planet’s internal workings and evolution.

Force on a Moving Charge in a Magnetic Field

The magnetic field exerts a force on a charge moving in the field because charges in motion constitute an electric current. E.g, the motion of electrons along conducting wires.

The strength of magnetic field, a vector quantity, is represented by Β, called the flux density or magnetic induction. If θ is the angle between the magnetic field direction and the direction of motion of the charges, then, the force, F on the charge is given by:

F=qvBsinθ

This force will be maximum when sin θ = 1 (i. e θ = 90⁰. The charge moves in a direction perpendicular to the magnetic field)

This force will be zero when θ = 0. (i.e the charge moves in the same direction as the magnetic field)

Where:

F is force in Newton,N

q is the charge in coulombs,C

v is the average velocity of the charge in m/s

B is the flux density or magnetic induction in tesla, T (1Tesla = 1Weber per m²).

Example:

Find the magnetic force experienced by an electron projected into a magnetic field of flux density 8Tesla with a velocity of 4.0 × 10⁶m/s and in the direction of 60°.

Solution:

F=qvBsinθF=1.6×10−19×4.0×106×8×sin60oF=4.43×10−12N

Note:

1. When an electron is projected perpendicular to the magnetic field, θ=900,∴sinθ=sin90o=1,Hence,F=qvB

2. When an electron is projected parallel to the magnetic field,

θ=0o,∴sinθ=sin0o=0, Hence,F=0

EVALUATION

1. State the formula for calculating the force on a charge moving in a magnetic field.
2. What is the value of F if an electron is projected parallel to the field?

GENERAL EVALUATION

1. Define angle of declination.
2. When F = 0, what is the value of θ and why?
3. What is the value of q?
4. Find the magnetic force experienced by an electron projected into a magnetic field of flux density 8Tesla with a velocity of 4.0 × 10⁶m/s and in the direction of 40° . Also find Fwhen the electron is projected normal to the field.
5. A force F projected an electron into a magnetic field of flux density 10 Tesla with a velocity of 2 × 10⁷m/s and normal to the field. (electron charge = 1.6 × 10^-19C). Find the magnetic force when the electron moves in direction parallel to the field. State the value of F if an electron is projected at 30° and 40°.
6. Overall, the magnetic field exerts a force on moving charges due to their motion through it. The strength of a magnetic field is measured by its flux density or magnetic induction, which is represented by the letter B. The force experienced by a moving charge in a magnetic field depends on its velocity, the strength of the magnetic field, and the angle between their directions. For maximum force, this angle is 90°; for no force, it is 0°. Additionally, q represents the charge of the moving charge in coulombs, and θ is the angle between its direction of motion and the magnetic field. To find the force on a particular charge in a specific situation, we can use the formula F = qvBsinθ, where v is velocity of the charge (in meters per second) and B is flux density or magnetic induction. Some examples include finding the force on an electron moving at a velocity of 4 × 106m/s and 60° to a magnetic field of 8T, and calculating the force when an electron moves parallel to the field. Similarly, we can find the value of F if an electron is projected at 30° or 40° by using trigonometric functions to determine the magnitude of the angle. Finally, we can evaluate a magnetic force by understanding the variables that affect its strength and direction, as well as calculating specific forces in given scenarios.