Problem 72-5    Source:  Problem 22.11 - page 18 - TIPLER, Paul - MOSCA, Gene -    Book: Física - Vol. 2 - 4ª Edição - Ed. LTC.

An electron enters a uniform electric field with E^→ = - 2,000   j^→ N/C and with initial speed v_o^→ = 10⁶   i^→ m/s perpendicular to the field.

a) compare the gravitational force acting on the electron to the electrical force in the field.

b) how much the electron will be deflected from the horizontal after advancing 1 cm in the direction x?

Solution of the Problem 72-5   

Item a   

To calculate the ratio between the electrical force F_e = - e E and the force gravitational F_g = m g , just calculate the quotient between them, or

Carrying out the calculation we find

Item b   

As the electron has a negative charge, it will travel in the opposite direction to the electric field, as we can see in the illustration of Figure 72-05.1.

The vertical deviation as a function of acceleration and time is given by

On the other hand, we know that t = x / v_o and also, a = (e E) / m. So, replacing in the equation of h, we get

By making the numerical substitution and performing the calculation, we find