To solve this problem we will apply the concepts related to the Electrostatic Force given by Coulomb's law. This force can be mathematically described as
![F = \frac{kq_1q_2}{d^2}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7Bkq_1q_2%7D%7Bd%5E2%7D)
Here
k = Coulomb's Constant
Charge of each object
d = Distance
Our values are given as,
![q_1 = 1 \mu C](https://tex.z-dn.net/?f=q_1%20%3D%201%20%5Cmu%20C)
![q_2 = 6 \mu C](https://tex.z-dn.net/?f=q_2%20%3D%206%20%5Cmu%20C)
d = 1 m
a) The electric force on charge
is
![F_{12} = \frac{ (9*10^9 Nm^2/C^2)(1*10^{-6} C)(6*10^{-6} C)}{(1 m)^2}](https://tex.z-dn.net/?f=F_%7B12%7D%20%3D%20%5Cfrac%7B%20%289%2A10%5E9%20Nm%5E2%2FC%5E2%29%281%2A10%5E%7B-6%7D%20C%29%286%2A10%5E%7B-6%7D%20C%29%7D%7B%281%20m%29%5E2%7D)
![F_{12} = 54 mN](https://tex.z-dn.net/?f=F_%7B12%7D%20%3D%2054%20mN)
Force is positive i.e. repulsive
b) As the force exerted on
will be equal to that act on
,
![F_{21} = F_{12}](https://tex.z-dn.net/?f=F_%7B21%7D%20%3D%20F_%7B12%7D)
![F_{21} = 54 mN](https://tex.z-dn.net/?f=F_%7B21%7D%20%3D%2054%20mN)
Force is positive i.e. repulsive
c) If
, a negative sign will be introduced into the expression above i.e.
![F_{12} = \frac{(9*10^9 Nm^2/C^2)(1*10^{-6} C)(-6*10^{-6} C)}{(1 m)^{2}}](https://tex.z-dn.net/?f=F_%7B12%7D%20%3D%20%5Cfrac%7B%289%2A10%5E9%20Nm%5E2%2FC%5E2%29%281%2A10%5E%7B-6%7D%20C%29%28-6%2A10%5E%7B-6%7D%20C%29%7D%7B%281%20m%29%5E%7B2%7D%7D)
![F_{12} = F_{21} = -54 mN](https://tex.z-dn.net/?f=F_%7B12%7D%20%3D%20F_%7B21%7D%20%3D%20-54%20mN)
Force is negative i.e. attractive
Answer:
Almost all machines require energy to offset the effects of gravity, friction, and air/wind resistance. Thus, no machine can continually operate at 100 percent efficiency.
Answer:
w = 11.211 KN/m
Explanation:
Given:
diameter, d = 50 mm
F.S = 2
L = 3
Due to symmetry, we have:
![Ay = By = \frac{w * 6}{2} = 3w](https://tex.z-dn.net/?f=%20Ay%20%3D%20By%20%3D%20%5Cfrac%7Bw%20%2A%206%7D%7B2%7D%20%3D%203w%20)
![P_c_r = 3w * F.S = 3w * 2.0 = 6w](https://tex.z-dn.net/?f=%20P_c_r%20%3D%203w%20%2A%20F.S%20%3D%203w%20%2A%202.0%20%3D%206w%20)
![I = \frac{\pi}{64} (0.05)^4 = 3.067*10^-^7](https://tex.z-dn.net/?f=%20I%20%3D%20%5Cfrac%7B%5Cpi%7D%7B64%7D%20%280.05%29%5E4%20%3D%203.067%2A10%5E-%5E7%20)
To find the maximum intensity, w, let's take the Pcr formula, we have:
![P_c_r = \frac{\pi^2 E I}{(KL)^2}](https://tex.z-dn.net/?f=%20P_c_r%20%3D%20%5Cfrac%7B%5Cpi%5E2%20E%20I%7D%7B%28KL%29%5E2%7D%20)
Let's take k = 1
Substituting figures, we have:
![6w = \frac{\pi^2 * 200*10^9 * 3.067*10^-^7}{(1 * 3)^2}](https://tex.z-dn.net/?f=%206w%20%3D%20%5Cfrac%7B%5Cpi%5E2%20%2A%20200%2A10%5E9%20%2A%203.067%2A10%5E-%5E7%7D%7B%281%20%2A%203%29%5E2%7D%20)
Solving for w, we have:
![w = \frac{67266.84}{6}](https://tex.z-dn.net/?f=%20w%20%3D%20%5Cfrac%7B67266.84%7D%7B6%7D%20)
w = 11211.14 N/m = 11.211 KN/m
Since Area, A= pi * (0.05)²
. This means it is safe
The maximum intensity w = 11.211KN/m