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Problem: What is the magnitude of the force F on the 5.0 nC charge in the figure? What is the direction of the force F on the 5.0 nC charge in the figure?

FREE Expert Solution

From Coulomb's law:

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

The angle between 5.0 nC and 10nC is obtained by:

θ = tan-1(4.0/3.0) = 53.1°

Force on 5nC due to 10nC:

$\begin{array}{rcl}{\mathbf{F}}_{\mathbf{1}}& \mathbf{=}& \frac{\mathbf{\left(}\mathbf{9}\mathbf{×}{\mathbf{10}}^{\mathbf{9}}\mathbf{\right)}\mathbf{\left(}\mathbf{5}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{\right)}\mathbf{\left(}\mathbf{10}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{\right)}}{{\mathbf{\left[}\sqrt{{\mathbf{\left(}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{×}\mathbf{10}\mathbf{-}\mathbf{2}\mathbf{\right)}}^{\mathbf{2}}\mathbf{+}{\left(3.0×10-2\right)}^{2}}\mathbf{\right]}}^{\mathbf{2}}}\mathbf{\left[}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\left(}\mathbf{53}\mathbf{.}\mathbf{1}\mathbf{°}\mathbf{\right)}\mathbf{\left(}\mathbf{-}\stackrel{\mathbf{^}}{\mathbf{i}}\mathbf{\right)}\mathbf{+}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\left(}\mathbf{53}\mathbf{.}\mathbf{1}\mathbf{°}\mathbf{\right)}\mathbf{\left(}\mathbf{-}\stackrel{\mathbf{^}}{\mathbf{j}}\mathbf{\right)}\mathbf{\right]}\end{array}$

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Problem Details

What is the magnitude of the force F on the 5.0 nC charge in the figure?

What is the direction of the force F on the 5.0 nC charge in the figure?

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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.

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