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36P

Expert-verifiedFound in: Page 125

Book edition
4th edition

Author(s)
Ruth W. Chabay, Bruce A. Sherwood

Pages
1135 pages

ISBN
9781118875865

**A proton and an electron are separated by ${\mathbf{1}}{\mathbf{\times}}{{\mathbf{10}}}^{\mathbf{-}\mathbf{10}}{\mathbf{}}{\mathbf{m}}$ the radius of a typical atom. Calculate the magnitude of the electric force that the proton exerts on the electron and the magnitude of the electric force that the electron exerts on the proton.**

The magnitude of the force that the proton exerts on the electron is $2.304\times {10}^{-8}\mathrm{N}$.

The magnitude of the force that the electron exerts on the proton is $2.304\times {10}^{-8}\mathrm{N}$.

**Coulomb's law is the most fundamental in electrostatics. This law determines the force one charged particle exerts over the other and vice versa. The physical expression of this law is:**

${\mathbf{F}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{4}{\mathbf{\pi \epsilon}}_{\mathbf{0}}}\frac{{\mathbf{q}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}^{\mathbf{2}}}$

**Here, r is the distance between two charged particles, and q is the charges.**

As it is known that the charge of the electron is ${\mathrm{q}}_{1}=-1.6\times {10}^{-19}\mathrm{C}$

It is also known the charge of the proton is data-custom-editor="chemistry" ${\mathrm{q}}_{2}=+1.6\times {10}^{-19}\mathrm{C}$

It is given that the separation between the electron and proton is data-custom-editor="chemistry" $\mathrm{r}=1\times {10}^{-10}\mathrm{m}$.

It is known that the force can be determined as:

data-custom-editor="chemistry" $\begin{array}{rcl}\left|\mathrm{F}\right|& =& \left|\frac{1}{4{\mathrm{\pi \epsilon}}_{0}}\frac{{\mathrm{q}}_{1}{\mathrm{q}}_{2}}{{\mathrm{r}}^{2}}\right|\\ & =& 9\times {10}^{9}\times \frac{{\left(1.6\times {10}^{-19}\right)}^{2}}{{\left(1\times {10}^{-10}\right)}^{2}}\\ & =& 2.304\times {10}^{-8}\mathrm{N}\end{array}$

As it is known that the charge of the electron is ${\mathrm{q}}_{1}=-1.6\times {10}^{-19}\mathrm{C}$

It is also known the charge of the proton is ${\mathrm{q}}_{2}=+1.6\times {10}^{-19}\mathrm{C}$

It is given that the separation between the electron and proton is $\mathrm{r}=1\times {10}^{-10}\mathrm{m}$

It is known that the force can be determined as:

$\begin{array}{rcl}\left|\mathrm{F}\right|& =& \left|\frac{1}{4{\mathrm{\pi \epsilon}}_{0}}\frac{{\mathrm{q}}_{1}{\mathrm{q}}_{2}}{{\mathrm{r}}^{2}}\right|\\ & =& 9\times {10}^{9}\times \frac{{\left(1.6\times {10}^{-19}\right)}^{2}}{{\left(1\times {10}^{-10}\right)}^{2}}\\ & =& 2.304\times {10}^{-8}\mathrm{N}\end{array}$

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