Calculating Electric Fields Using Coulomb's Law

[AbbyGirl]

Homework Statement

Use Coulomb's law to determine the magnitude and direction of the electric field at points A and B in Fig. 16-57 due to the two positive charges (Q = 4.0 µC) shown.

The Attempt at a Solution

Basically, I'm completely lost. I've applied Coulomb's law to find the magnitudes of the contributing electric fields.

Can anyone help me solve this problem/ at least get started. Thanks so much, god bless.

 

[Copycat91]

Apply Coulomb's law for each charge separately.
Then use vector superposition once you find electric field for each charge.

 

[chrisk]

An electric field is a vector so it has a magnitude and a direction. Using Coulomb's Law gives an expression for E:

$$\vec{E}=\frac{\vec{F}}{q}\mbox{ where q is a test charge}$$

$$\vec{F}=\frac{qQ\hat{r}}{4\pi \varepsilon_0 \ r^2}$$

$$\mbox{where }\hat{r}\mbox{ is the unit vector in the r direction}$$

So,

$$\vec{E}=\frac{Q\hat{r}}{4\pi \varepsilon_0 \ r^2}$$

where r is the distance from the charge to the point in question. Resolve E into E_x and E_y using cosine and sine. Then add these resolved components to find the resultant components.