Understanding Magnetic Fields: Definitions and Applications
Magnetic Field: Definitions and Applications
Magnetism, just as electricity, is a property that all materials possess to a greater or lesser extent. This property consists of performing actions from a distance, such as attracting and repelling, plus producing induced electric currents.
Despite the force between two electric charges behaving the same as the force between two magnetic poles, unlike electricity, an individual magnetic pole cannot be separated: poles are always found in pairs.
For example, you can split any magnet into a thousand parts, but each part will have a north and south pole.
As we learned during our study of electricity, an electric field surrounds every electric charge, whether it is at rest or in motion. Electric charges in motion also have a magnetic field that surrounds them. To describe their behavior, there are flow lines (such as the lines for an electric field).
So, if two equal magnetic poles are placed near each other, both are repelled, but if two different magnetic poles are placed near each other, both are attracted, as seen in the figure shown below.
The density of a magnetic flow (B) is the number of flow lines (Φ) per area unit (A) perpendicular to the electric field’s region. Its unit of measurement in the international system is the Tesla (T), while the unit of measurement for flow lines is the Weber (Wb).
Example 11.1
Calculate the magnetic flow that goes through a plate 5 cm long by 7 cm wide if the flow density is .5T.
Answer:
Clearing out the flow from the previous formula, we have that:
A magnetic force is applied on a charge when this goes through a magnetic field; it is perpendicular both to the magnetic flow density 
and to the speed 
of the charge in motion.
The direction of a magnetic force 
under a positive charge in motion with a speed on a field with a flow density can be calculated by the right hand rule.
Giancoli, D. (2005). Physics: Principles with applications. (6th edition). Prentice Hall, New Jersey (p. 558)
- Force on a current-carrying wire placed in a magnetic field.
- Same, but current reversed.
- Right-hand rule for setup in (b).
Where q is the change’s value that goes through the field.
Example 11.2
A proton on an electric field moves front in direction +x at a speed of 10,000 m/s. The electric field is found in direction +y and has a magnitude of .03 T. Find the magnetic force’s value and its direction.
Answer:
A proton’s charge is 
Using the formula previously seen, we have:
Using the right hand rule, we find that the direction is +z.
When we have a conductor by which current flows, a magnetic force is applied and it is obtained by:
Where 
is the current’s magnitude, and 
is the conductor’s length.
Example 11.3
A wire with a 15 cm length forms an angle of 90° with a field of .5T. Through the wire a 7A current flows. What is the magnitude and direction of the resulting force?
Answer:
Using the right hand rule, we have that the direction is upwards.
Earth is surrounded by a magnetic field and its poles vary during the year as a consequence of the motion produced within.
The Earth acts like a huge magnet; but its magnetic poles are not at the geographic poles, which are on the Earth’s rotation axis.
Giancoli, D. (2005). Physics: Principles with applications. (6th edition). Prentice Hall, New Jersey (p. 556)
Ampere’s Law
Ampere’s Law allows us to calculate the magnetic field produced by a distribution of electric currents when such a field has certain symmetry.
Where 
is the sum of the electric field parallel to the length 
is the total electric current in the chosen closed trajectory, µ is the permeability of the medium that surrounds the wire. When the medium is the void, the air or non-magnetic media:
To calculate the magnetic field on a long straight wire, a circular trajectory is used around the current flow and Ampere’s Law results as:
Example 11.4
Calculate the magnetic field on a 1m long wire, in which a 5A current flows.
Answer:
We choose to imagine a closed trajectory in the shape of a circle and Ampere’s Law would then be:
