Answer:
![\rm EPE_{final}-EPE_{initial}=-1.478\times 10^{-15}\ J.](https://tex.z-dn.net/?f=%5Crm%20EPE_%7Bfinal%7D-EPE_%7Binitial%7D%3D-1.478%5Ctimes%2010%5E%7B-15%7D%5C%20J.)
Explanation:
Given charges are:
![\rm q_1 = +6e.\\q_2 = -6e.](https://tex.z-dn.net/?f=%5Crm%20q_1%20%3D%20%2B6e.%5C%5Cq_2%20%3D%20-6e.)
The electric potential energy of a charge due to the electric field of another charge is given by
![\rm EPE=\dfrac{kq_1q_2}{r}.](https://tex.z-dn.net/?f=%5Crm%20EPE%3D%5Cdfrac%7Bkq_1q_2%7D%7Br%7D.)
where,
- k = Coulomb's constant, having value =
![\rm 9\times 10^9\ Nm^2/C^2.](https://tex.z-dn.net/?f=%5Crm%209%5Ctimes%2010%5E9%5C%20Nm%5E2%2FC%5E2.)
- r = distance between the charges.
When the charges are infinite distance apart,
,
![\rm EPE_{initial} = \dfrac{kq_1q_2}{r}=0\ J.](https://tex.z-dn.net/?f=%5Crm%20EPE_%7Binitial%7D%20%3D%20%5Cdfrac%7Bkq_1q_2%7D%7Br%7D%3D0%5C%20J.)
When the charges are
apart,
,
![\rm EPE_{final}=\dfrac{kq_1q_2}{r}\\=\dfrac{(9\times 10^9)\times (+6e)\times (-6e)}{5.61\times 10^{-12}}\\=-5.775\ e^2\times 10^{22}.](https://tex.z-dn.net/?f=%5Crm%20EPE_%7Bfinal%7D%3D%5Cdfrac%7Bkq_1q_2%7D%7Br%7D%5C%5C%3D%5Cdfrac%7B%289%5Ctimes%2010%5E9%29%5Ctimes%20%28%2B6e%29%5Ctimes%20%28-6e%29%7D%7B5.61%5Ctimes%2010%5E%7B-12%7D%7D%5C%5C%3D-5.775%5C%20e%5E2%5Ctimes%2010%5E%7B22%7D.)
Here, e is the charge on one electron, such that,
.
Therefore,
![\rm EPE_{final}=-5.775\times (-1.6\times 10^{-19})^2\times 10^{22} = -1.478\times 10^{-15}\ J.](https://tex.z-dn.net/?f=%5Crm%20EPE_%7Bfinal%7D%3D-5.775%5Ctimes%20%28-1.6%5Ctimes%2010%5E%7B-19%7D%29%5E2%5Ctimes%2010%5E%7B22%7D%20%3D%20-1.478%5Ctimes%2010%5E%7B-15%7D%5C%20J.)
Thus,
![\rm EPE_{final}-EPE_{initial}=-1.478\times 10^{-15}-0=-1.478\times 10^{-15}\ J.](https://tex.z-dn.net/?f=%5Crm%20EPE_%7Bfinal%7D-EPE_%7Binitial%7D%3D-1.478%5Ctimes%2010%5E%7B-15%7D-0%3D-1.478%5Ctimes%2010%5E%7B-15%7D%5C%20J.)
Low-level nuclear waste can be disposed of in a landfill.
Current is measured as charge per unit time. To get change, simply multiply the current with time:
Answer:
The right answer for this question is 85%.
(I had the same question.)
Incomplete question as the angle between the force is not given I assumed angle of 55°.The complete question is here
Two forces, a vertical force of 22 lb and another of 16 lb, act on the same object. The angle between these forces is 55°. Find the magnitude and direction angle from the positive x-axis of the resultant force that acts on the object. (Round to one decimal places.)
Answer:
Resultant Force=33.8 lb
Angle=67.2°
Explanation:
Given data
Fa=22 lb
Fb=16 lb
Θ=55⁰
To find
(i) Resultant Force F
(ii)Angle α
Solution
First we need to represent the forces in vector form
![\sqrt{x} F_{1}=22j\\ F_{2}=u+v\\F_{2}=16sin(55)i+16cos(55)j\\F_{2}=16(0.82)i+16(0.5735)j\\F_{2}=13.12i+9.176j](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20F_%7B1%7D%3D22j%5C%5C%20F_%7B2%7D%3Du%2Bv%5C%5CF_%7B2%7D%3D16sin%2855%29i%2B16cos%2855%29j%5C%5CF_%7B2%7D%3D16%280.82%29i%2B16%280.5735%29j%5C%5CF_%7B2%7D%3D13.12i%2B9.176j)
Total Force
![F=F_{1}+F_{2}\\ F_{2}=22j+13.12i+9.176j\\F_{2}=13.12i+31.176j](https://tex.z-dn.net/?f=F%3DF_%7B1%7D%2BF_%7B2%7D%5C%5C%20F_%7B2%7D%3D22j%2B13.12i%2B9.176j%5C%5CF_%7B2%7D%3D13.12i%2B31.176j)
The Resultant Force is given as
![|F|=\sqrt{x^{2} +y^{2} }\\|F|=\sqrt{(13.12)^{2} +(31.176)^{2} }\\ |F|=33.8lb](https://tex.z-dn.net/?f=%7CF%7C%3D%5Csqrt%7Bx%5E%7B2%7D%20%2By%5E%7B2%7D%20%7D%5C%5C%7CF%7C%3D%5Csqrt%7B%2813.12%29%5E%7B2%7D%20%2B%2831.176%29%5E%7B2%7D%20%7D%5C%5C%20%7CF%7C%3D33.8lb)
For(ii) angle
We can find the angle bu using tanα=y/x
So
![tan\alpha =\frac{31.176}{13.12}\\ \alpha =tan^{-1} (\frac{31.176}{13.12})\\\alpha =67.2^{o}](https://tex.z-dn.net/?f=tan%5Calpha%20%3D%5Cfrac%7B31.176%7D%7B13.12%7D%5C%5C%20%5Calpha%20%3Dtan%5E%7B-1%7D%20%28%5Cfrac%7B31.176%7D%7B13.12%7D%29%5C%5C%5Calpha%20%3D67.2%5E%7Bo%7D)