# 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 ).