Physics, 17.10.2021 14:00 vett072804
The magnitude of the electrostatic force between two point charges Q and q of the same sign is given by F(x) = KQq/x², where x is the distance between the charges and K = 9 × 10⁹ N•m²/C² is a physical constant ( C stands for Coulomb, the unit of charge & N stands for Newton, the unit of force ).
A.) Find the instantaneous rate of change of the force with respect to the distance between the charges.
B.) For two identical charges with Q = q = 2C, what is the instantaneous rate of change of the force at a separation of x = 0.001m ?
Answers: 3
assuming that the units of 
and 
are both coulomb.
, then 
. 
. 
.
with respect to 
to find the corresponding instantaneous rate of change.![\begin{aligned} \frac{d}{dx}\, \left[x^{-2}\right] &= (-2)\, x^{-3} \end{aligned}](/tpl/images/2510/1162/ed928.png)
.![\begin{aligned}F^{\prime}(x) &= \frac{d}{dx}\left[k\cdot Q \cdot q \cdot x^{-2}\right] \\ &= k \cdot Q \cdot q \cdot \frac{d}{dx} \left[x^{-2}\right] \\ &= (-2)\, k \cdot Q \cdot q \cdot x^{-3} \\ &= \frac{(-2)\, k \cdot Q \cdot q}{x^{3}}\end{aligned}](/tpl/images/2510/1162/5efd6.png)
.
. Assume that the units of 
into the expression for 
:
.
, 
, and 
into the expression and evaluate:
.
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