Problem 71-8
Source: Adapted of the Problem 76 - page 817 - KNIGHT, Randall D. -
Book:
Física - Uma Abordagem Estratégica - 2ª Edição - Ed. Bookman - 2009.
In Figure 71-08.1 a force F = 1.94 x 10 -4N, represented on the charge of
- 1 nC.
Determine the nature of the charge q and its value, as well as the value of the force
attraction or repulsion on the negative charge.
Solution of the Problema 71-8
First, let's determine the distances between charges. The negative charge is far from the positive
charge of d1 = 5 cos 60° = 2.5 cm = 2.5 x 10 -2 m . And the negative charge is far from the charge q of
d2 = 5 cos 30° = 2.5 x √ 3 cm = 2.5 x √ 3 x 10-2m .
Now, using Coulomb's law we can calculate the force of attraction, which we will call
F1, between the negative charge and the positive charge. Like this:
Performing the calculation we find
On the other hand, analyzing Figure71-08.1, we conclude that for the resulting force F
that acts on the negative charge is pointing down, the charge q must be
positive to generate a force of attraction F2. Also, from the figure,
we realize that the forces
F1 and F2 make an angle of 90° to each other. So,
to determine the value
of F2 we can use the Pythagoras theorem. Soon
Substituting the numerical values and performing the calculation, we obtain:
Therefore, we already know the value of the force F2 = 1.30 x 10-4 N
and also its nature, which must be a positive charge. We just need to calculate the value of the charge
q . For that we will use the law of Coulomb, making an algebraic rearrangement
in such a way that
Substituting the numerical values and performing the calculation, we obtain:
