Problem 74-3    Source:   List of PUC-Goiás - Problem 20 - Prof. Renato Medeiros - 2014.

A long straight wire carries an electrical current of 50 A horizontally to the right. An electron is moving at a speed of 1.0 x 10⁷ m/s when passing 5 cm of that wire, as shown in Figure 74-03.1 . What force will act over the electron if its velocity is oriented:

a) horizontally to the right (represented by v₁ in the figure).

b) vertically upwards (represented by v₂ in the figure).

Solution del Problem 74-3   

Item a   

To determine the force acting on the electron, we must first calculate the value of the magnetic induction vector at the electron position. As was studied in item 2.4, the magnetic induction vector produced by a long straight wire is given by eq. 74-17, reproduced below.

Then, substituting the numerical values and performing the calculation, we obtain:

From Figure 74-03.1, we can easily see that the angle formed by the magnetic induction vector and the direction of electron displacement is equal to 90°. And to determine the magnetic force to which the electron is subjected, we will use eq. 74-02, as studied in item 2. For further understanding we will reproduce it below.

Recalling that q = 1.60 x 10^-19 C and sen 90° = 1 , then replacing by numerical values, we have:

Thus, performing the calculation, we find:

To determine the direction and orientation of the magnetic force, just apply the right hand rule and verify that the force points to the right, forcing the electron to move away from the wire.

Item b   

In case the electron is moving vertically upwards, as shown in Figure 74-03.1, we clearly perceive that the velocity vector is going in the opposite direction to the magnetic induction vector. Therefore, the angle formed between them is equal to θ = 180°. And we know that sen 180 ° = 0 . So the magnetic force on the electron is zero.