Coulomb's Law (Electric Force) Video Lessons

Concept

# Problem: 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 2Q. Express your answer in terms of Coulomb's constant k, Q, and l.b. Determine the direction of the force on the charge 2Q. Express your answer using two significant figures.

###### FREE Expert Solution

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:

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

F2Qx = 4.828 kQ2/l2

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###### Problem Details

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 2Q. Express your answer in terms of Coulomb's constant k, Q, and l.

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