Vector Magnetic Field

In the study of electricity, we saw that when we place a test charge q at a point P in a region where there is an electric field , a force of electrical origin  exerted by the electric field begins to act on the test charge. Thus, the electric field was defined as follows:

On what:

In the SI, the unit of the electric field vector  is N/C (newton/coulomb).

The test charge is an electrically charged particle with negligible dimensions, in addition to being used to detect if there is an electric field at a given location. However, in magnetism, you do not have a magnetized charge and the determination of the magnetic field is  not the same.

Thus, the definition of the magnetic field starts from the interaction between the magnetic field and a moving test charge.

1 that when a test charge q moving with velocity  at a point P is acted upon by a force  perpendicular to , a magnetic field vector , which forms an angle θ with the velocity vector , is associated with that point . Thus, the magnetic field , in module, is defined as:

On what:

The SI unit of magnetic field and, in honor of physicist Nikola Tesla, is named tesla (T).

Since the magnetic field is a vector quantity, it necessarily has a magnitude, a direction and a sense. Thus, the modulus is given by equation 2, and the direction will be given by the right-hand rule.

Right Hand Rule

The right hand rule gives us the information as follows:

  • The thumb indicates the direction of  the test load velocity;
  • With the palm extended, the fingers indicate the direction of the magnetic field vector ;
  • Perpendicularly to the palm of the hand, the force comes out . Note that if the test charge is negative, the force  is in reverse.

Note that the force  will always be perpendicular to the plane formed by​ and 

From the definition of the magnetic field, one can derive the expression of the magnetic force:

Magnetic Force:

F=qvB .sin θ

Equation 3: Magnetic Force

From equation 3, it can be seen that the magnetic force will have its maximum value when θ=90°, therefore, F=qvB, since sin 90°=1. Its value will be minimum when θ=0° or 180°, since sin 0°=sin 180°=0, which implies a null magnetic force F = 0 (this occurs when the velocity and the magnetic field vector are in the same direction ).

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