Coulomb's law:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}^{\mathbf{2}}}}$

**a.**

The x-component of the force:

$\begin{array}{rcl}{\mathbf{F}}_{\mathbf{2}\mathbf{Q}\mathbf{x}}& \mathbf{=}& \frac{\mathbf{k}\mathbf{\left(}\mathbf{2}\mathbf{Q}\mathbf{\right)}\mathbf{\left(}\mathbf{Q}\mathbf{\right)}}{{\mathbf{l}}^{\mathbf{2}}}\mathbf{+}\frac{\mathbf{k}\mathbf{\left(}\mathbf{2}\mathbf{Q}\mathbf{\right)}\mathbf{\left(}\mathbf{4}\mathbf{Q}\mathbf{\right)}}{\mathbf{2}{\mathbf{l}}^{\mathbf{2}}}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{(}\mathbf{45}\mathbf{\xb0}\mathbf{)}\\ & \mathbf{=}& \frac{\mathbf{k}{\mathbf{Q}}^{\mathbf{2}}}{{\mathbf{l}}^{\mathbf{2}}}\mathbf{(}\mathbf{2}\mathbf{+}\mathbf{2}\sqrt{\mathbf{2}}\mathbf{)}\end{array}$

F_{2Qx} = 4.828 kQ^{2}/l^{2}

At each corner of a square of side *l* there are point charges of magnitude Q, 2Q, 3Q, and 4Q.

a. Determine the magnitude of the force on the charge 2*Q*.** **Express your answer in terms of Coulomb's constant *k*, *Q*, and *l*.

b. Determine the direction of the force on the charge 2*Q.* Express your answer using two significant figures.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Coulomb's Law (Electric Force) concept. You can view video lessons to learn Coulomb's Law (Electric Force). Or if you need more Coulomb's Law (Electric Force) practice, you can also practice Coulomb's Law (Electric Force) practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor McCormick's class at USF.