Problem 74-1    Source:  Problem developed by the site author.

A positively charged particle, as shown in Figure 74-01.1 , with mass equal to m = 5 x 10^-7 Kg and equal load a q = 10^-4 C , when passing through a hole in a bulkhead, penetrates an environment that is under the action of a magnetic induction field of B = 2.5 T. Alongside the bulkhead, there is a target that is 80 cm from the bulkhead. If, when passing through the orifice, the particle a speed of v = 500 m/s, determine:

a) What lateral distance from the orifice will the particle collide with the target?

b) The particle's trajectory (show through a diagram).

Problem 74-2    Source:   Problem developed by the site author.

A proton with a kinetic energy equal to 7 MeV is launched horizontally into a laboratory chamber that has a magnetic induction field equal to 2.80 T . This field is oriented vertically downwards and the proton moves from left to right, as shown in Figure 74-02.1 . Considering the mass of the proton equal to 1.67 x 10^-27 Kg, determine:

a) The force that the proton experiences when entering the chamber.

b) Calculate the radius of the circumference that the proton describes.

c) Calculate the proton angular frequency.

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).

Problem 74-4    Source:   Problem developed by the site author.

A 100 kV transmission line must be installed along a river bank. It is known that the river undergoes a dredging process periodically, in order to clean the along its course. The machines used do not work properly if they are exposed to magnetic fields greater than 4 µ T. If at peak energy consumption the current can reach values of 200 A, determine the minimum height of the transmission line (Disregard the Earth's magnetic field).

Problem 74-5    Source:   Problem 25 - page 227 -    HALLIDAY, RESNICK, WALKER, Jearl -   Book: Fundamentos de Física - Vol 3 - Ed. LTC - 8ª edição - 2009.

A alpha particle, where q = +2 e and m = 4.00 u describes a circular path of 4.50 cm in radius in a region where there is a uniform magnetic induction field of modulus equal to B = 1.20 T. Determine:

a) the scalar velocity of the particle.

b) the period of revolution.

c) the kinetic energy of the alpha particle.

d) the potential difference necessary for the particle to reach the energy of item c).

Problem 74-6    Source:   Problem 27 - page 227 -    HALLIDAY, RESNICK, WALKER, Jearl -   Book: Fundamentos de Física - Vol 3 - Ed. LTC - 8ª edição - 2009.

An electron describes a helical path in a uniform magnetic induction field of modulus equal to 0.30 T. The pitch of the helix is 6.00 µm , and the magnitude of the magnetic force experienced by the electron is equal to 2.00 x 10^-15 N . What is the speed of the electron?

Problem 74-7    Source:   Adapted of the example 22.8 - page 162 -    SERWAY, Raymond A. -   Book: Princípios de Física - Vol 3 - Ed. Cengage Learning - 5ª edição - 2014.

Be a long, straight wire with a radius of R = 1 cm and being traversed by a stationary current with a value equal to I = 100 A, evenly distributed across the cross section of the wire, as shown in Figure 74-07.1. Determine:

a) the magnetic induction field at a distance r from the center of the wire, being r < R.

b) the same calculation considering r > R.

c) show in a graph the behavior of B as a function of r.

Problem 74-8    Source:   Problem elaborated by the author of the site.

An enameled wire of 17 AWG gauge is used, which has a diameter of 1.15 mm and can be conduct, at most, a current of 3.2 A, for the construction of a coil formed by 400 turns in a cylindrical shape 10 cm in diameter. Determine.

a) the maximum voltage that can be applied to the coil.

b) in this case, what is the value of the magnetic induction field.

Problem 74-9    Source:   List of PUC-Goiás - Problem 23 - page 14 - Prof. Renato Medeiros - 2014.

Two coils or solenoids, 1 and 2, are connected to a battery in the series configuration, as shown in Figure 74-09.1, with no type of magnetic coupling between them. The two coils have 100 turns and whose length is L₁ = 20 cm and L₂ = 40 cm. Ask if:

a) the electric current through the coil 1 is greater, less than or equal to the electric current circulating through the coil 2?

b) the magnetic induction field inside the coil 1 is greater, less than or equal to magnetic induction field inside the coil 2?

c) know that B₁ = 6,0 mT, what is the value of B₂?