Effects of a magnetic field on charges

Electric charge with speed in different direction from electric field

When a charge is abandoned in the vicinity of a stationary magnetic field with velocity in a different direction from the field, it interacts with it. Then this force will be given by the product between the two vectors, and and will result in a third vector perpendicular to both, this is called a vector product and is a vector operation that is not seen in high school.

But we can divide this study into a peculiar case where the charge moves perpendicular to the field, and another where the direction of motion is any except equal to that of the field.

  • Load with perpendicular movement to the field

Experimentally it can be observed that if we approach a magnet of electric charges with movement perpendicular to the magnetic field, this movement will be shifted perpendicular to the field and the velocity, that is, up or down. This will be the direction of the magnetic force vector.

For positive charges this deviation happens upwards:

And for negative charges down.

The intensity of will be given by the vector product which for the particular case where and are perpendicular is calculated by:

The unit adopted for magnetic field intensity is tesla (T), which he calls , in honor of Yugoslav physicist Nikola Tesla.

Consequently the force will be calculated by:

Measured in newtons (N)

  • Load moving with arbitrary direction to field

As mentioned earlier, the case where the charge has perpendicular motion to the field is just a peculiarity of interaction between charge and magnetic field. For the other cases the direction of the vector will be perpendicular to the magnetic field vector and at speed vector .

For the calculation of the intensity of the magnetic field only the component of the velocity perpendicular to the field is considered, that is, , being the angle formed between and so replacing v by its perpendicular component we will have:

Applying this law to the other cases we saw earlier, we will see that:

  • if v = 0, then F = 0
  • if = 0 ° or 180 °, then sen = 0, so F = 0
  • if = 90 °, then sen = 1, so .

Right hand rule

A method used to determine the direction of the vector is the so-called flat right hand rule. With an open hand, your thumb is pointing towards the speed vector and the other fingers towards the magnetic field vector.

For positive charges, vector will have the direction of a line that runs through the hand, and its meaning will be that of a vector that comes out of the palm.

For negative charges, vector it will have the direction of a line that runs through the hand, and its meaning will be that of a vector that comes out of the back of the hand, that is, the vector that enters the palm.