Answer:
x = 1.00486 m
Explanation:
The complete question is:
" The potential energy between two atoms in a particular molecule has the form U(x) =(2.6)/x^8 −(5.1)/x^4 where the units of x are length and the num- bers 2.6 and 5.1 have appropriate units so that U(x) has units of energy. What is the equilibrium separation of the atoms (that is the distance at which the force between the atoms is zero)? "
Solution:
- The correlation between force F and energy U is given as:
F = - dU / dx
F = - d[(2.6)/x^8 −(5.1)/x^4] / dx
F = 20.8 / x^9 - 20.4 / x^5
- The equilibrium separation distance between atoms is given when Force F is zero:
0 = 20.8 / x^9 - 20.4 / x^5
0 = 20.8 - 20.4*x^4
x^4 = 20.8/20.4
x = ( 20.8/20.4 )^0.25
x = 1.00486 m
The object is at rest is the answer.
Complete Question
A thin, horizontal, 12-cm-diameter copper plate is charged to 4.4 nC . Assume that the electrons are uniformly distributed on the surface. What is the strength of the electric field 0.1 mm above the center of the top surface of the plate?
Answer:
The values is 
Explanation:
From the question we are told that
The diameter is 
The charge is 
The distance from the center is 
Generally the radius is mathematically represented as

=> 
=> 
Generally electric field is mathematically represented as
![E = \frac{Q}{ 2\epsilon_o } [1 - \frac{k}{\sqrt{r^2 + k^2 } } ]](https://tex.z-dn.net/?f=E%20%3D%20%20%5Cfrac%7BQ%7D%7B%202%5Cepsilon_o%20%7D%20%5B1%20-%20%5Cfrac%7Bk%7D%7B%5Csqrt%7Br%5E2%20%2B%20%20k%5E2%20%7D%20%7D%20%5D)
substituting values
![E = \frac{4.4 *10^{-9}}{ 2* (8.85*10^{-12}) } [1 - \frac{(1.00 *10^{-4})}{\sqrt{(0.06)^2 + (1.0*10^{-4})^2 } } ]](https://tex.z-dn.net/?f=E%20%3D%20%20%5Cfrac%7B4.4%20%2A10%5E%7B-9%7D%7D%7B%202%2A%20%288.85%2A10%5E%7B-12%7D%29%20%7D%20%5B1%20-%20%5Cfrac%7B%281.00%20%2A10%5E%7B-4%7D%29%7D%7B%5Csqrt%7B%280.06%29%5E2%20%2B%20%20%281.0%2A10%5E%7B-4%7D%29%5E2%20%7D%20%7D%20%5D)

Clearly visible data points and appropriate labels on each access that include units