Problem 71-3    Source:  Problem developed by the author of the site.

Whether it's two charges, q₁ = 20 µC in the coordinate (0,-5) meters and q₂ = - 10 µC in the coordinate (-5,0) meters. Calculate:

a) What is the electric field produced by these charges at the source?

b) The resulting electric field and its angle with the positive x-axis.

Solution of the Problem 71-3   

Item a

To solve this problem we will refer to the diagram shown opposite. Notice that the field produced by the positive charge (red vector) is moving away from the charge, according to the adopted convention. And the field produced by the negative charge (blue vector) is pointing towards it. With this we have two vectors that form an angle of 90° to each other. To calculate the resulting electric field we can apply the Pythagorean theorem.

For this we will calculate the values of E₁ and E₂ using the eq. 71-05.

Performing the calculation we find:

For the calculation of E₂ we have:

Performing the calculation we find:

Item b

Now we can calculate the value of E_R using the Pythagorean theorem, or:

Substituting for the numerical values and performing the calculation we find:

And to calculate the angle θ , by the figure above, we have the following relation:

So, initially calculating the value of φ, we have:

So now we can calculate the value of θ, or: