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How far apart must two point charges of 75.0 nC (typical of static electricity) be to have a force of 1.00 N between them?
If two equal charges each of 1 C each are separated in air by a distance of 1 km, what is the magnitude of the force acting between them? You will see that even at a distance as large as 1 km, the repulsive force is substantial because 1 C is a very significant amount of charge.
A test charge of $\mathrm{+2}\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ is placed halfway between a charge of $\mathrm{+6}\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ and another of $\mathrm{+4}\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ separated by 10 cm. (a) What is the magnitude of the force on the test charge? (b) What is the direction of this force (away from or toward the $\mathrm{+6}\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ charge)?
Bare free charges do not remain stationary when close together. To illustrate this, calculate the acceleration of two isolated protons separated by 2.00 nm (a typical distance between gas atoms). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.
$\begin{array}{lll}F& =& k\frac{\left|{q}_{1}{q}_{2}\right|}{{r}^{2}}=\mathrm{ma}\Rightarrow a=\frac{k{q}^{2}}{m{r}^{2}}\\ & =& \frac{(9.00\times {10}^{9}\phantom{\rule{0.25em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2}){(1.60\times {10}^{\mathrm{\u201319}}\phantom{\rule{0.25em}{0ex}}\text{m})}^{2}}{(1.67\times {10}^{\mathrm{\u201327}}\phantom{\rule{0.25em}{0ex}}\text{kg}){(2.00\times {10}^{\mathrm{\u20139}}\phantom{\rule{0.25em}{0ex}}\text{m})}^{2}}\\ & =& 3.45\times {10}^{16}\phantom{\rule{0.25em}{0ex}}\text{m/}{\text{s}}^{2}\end{array}$
(a) By what factor must you change the distance between two point charges to change the force between them by a factor of 10? (b) Explain how the distance can either increase or decrease by this factor and still cause a factor of 10 change in the force.
(a) 3.2
(b) If the distance increases by 3.2, then the force will decrease by a factor of 10 ; if the distance decreases by 3.2, then the force will increase by a factor of 10. Either way, the force changes by a factor of 10.
Suppose you have a total charge ${q}_{\text{tot}}$ that you can split in any manner. Once split, the separation distance is fixed. How do you split the charge to achieve the greatest force?
(a) Common transparent tape becomes charged when pulled from a dispenser. If one piece is placed above another, the repulsive force can be great enough to support the top piece’s weight. Assuming equal point charges (only an approximation), calculate the magnitude of the charge if electrostatic force is great enough to support the weight of a 10.0 mg piece of tape held 1.00 cm above another. (b) Discuss whether the magnitude of this charge is consistent with what is typical of static electricity.
(a) $1\text{.}\text{04}\times {\text{10}}^{-9}$ C
(b) This charge is approximately 1 nC, which is consistent with the magnitude of charge typical for static electricity
(a) Find the ratio of the electrostatic to gravitational force between two electrons. (b) What is this ratio for two protons? (c) Why is the ratio different for electrons and protons?
At what distance is the electrostatic force between two protons equal to the weight of one proton?
A certain five cent coin contains 5.00 g of nickel. What fraction of the nickel atoms’ electrons, removed and placed 1.00 m above it, would support the weight of this coin? The atomic mass of nickel is 58.7, and each nickel atom contains 28 electrons and 28 protons.
$1\text{.}\text{02}\times {\text{10}}^{-\text{11}}$
(a) Two point charges totaling $8.00\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ exert a repulsive force of 0.150 N on one another when separated by 0.500 m. What is the charge on each? (b) What is the charge on each if the force is attractive?
Point charges of $5.00\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ and $\mathrm{\u20133.00}\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ are placed 0.250 m apart. (a) Where can a third charge be placed so that the net force on it is zero? (b) What if both charges are positive?
Two point charges ${q}_{\text{1}}$ and ${q}_{\text{2}}$ are $\mathrm{3.00\; m}$ apart, and their total charge is $20\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ . (a) If the force of repulsion between them is 0.075N, what are magnitudes of the two charges? (b) If one charge attracts the other with a force of 0.525N, what are the magnitudes of the two charges? Note that you may need to solve a quadratic equation to reach your answer.
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