Answer to Question #234975 in Physics for Soriano

Question

Supposed a charge is at the origin

Determine the direction angle of the electric field at the point( 0.9, 1.2) measured counterclockwise from the positive x axis if the particle is negatively charged?

Answer 1

The electric field vector at point ( 0.9, 1.2) is denoted as $\vec{E}$ (since the charge is point and negative, it is directed toward the charge). The angle that is required to find is $\theta$.

From the right triangle, obtain:

$$\beta = 90\degree -\alpha$$

In turn:

$$\theta = 360\degree -90\degree - \beta = 180+\alpha$$

Angle $\alpha$ is given as follows:

$$\alpha = \arctan\left( \dfrac{1.2}{0.9} \right) \approx 53\degree$$

Thus, obtain:

$$\theta = 180\degree + 53\degree = 233\degree$$

Answer. $233\degree$.