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?

Solution of the Problema 74-9   

Item a   

As the coils are connected in series configuration, it is obvious that the intensity of currents flowing through the coils are equal.

Item b   

In this item we will analyze the magnetic induction field of the solenoid (coil) using the eq. 74-23 reproduced below:

Note that, since coil 1 has a shorter length for the same number of turns, so by eq. 74-23 it is noticed that the magnetic induction field will be larger in this coil.

Item c   

Based on what was said in the previous item, we can easily see that the magnetic induction field in the coil 2 is half of the field in coil 1, that is, B₂ = 3 mT , because we know that the electric current and the number of turns are the same in the two coils, but the length of coil 2 is twice the length of coil 1.