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?

Solution of the Problem 74-6   

Using the eq. 74-02, reproduced below, we can calculate the speed orthogonal to the movement.

After algebraic manipulation, we have:

We use the fact that sen 90° = 1. So, replacing with the numerical values we have:

Performing the calculation, we obtain:

Now we need to calculate the parallel component of the velocity. To do this, we will use the eq. 74-07a, reproduced below.

But first it is necessary to calculate the period of the movement, using the eq. 74-06 , reproduced below.

Substituting for numeric values, we have:

Performing the calculation, we obtain:

Therefore, rearranging the terms of equation eq. 74-07a and replacing with the numerical values, we have:

Performing the calculation, we obtain:

Now that we have found the values of the two components of the velocity, we must add them vectorally, finding:

Performing the calculation, we obtain: