Energy of Electron: Solving Eqn & Variable k

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The variable k in the equation E=(p^{2}/2m)-(ke^{2}/r) represents the Coulomb's Law constant, specifically k=1/4πε₀, where ε₀ is the permittivity of free space valued at approximately 8.85X10^-12. This constant is crucial for calculating the electrostatic force between charged particles, similar to how G functions in Newton's Law of Gravity. The numerical value of k is around 9X10^9 Nm²/C². The discussion clarifies that some textbooks may use 'k' interchangeably with the expression for Coulomb's constant. Understanding this relationship is essential for solving problems related to the energy of electrons in electric fields.
patapat
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So I'm staring at this equation in my book and I am not sure what the variable k represents in this equation: E=(p^{2}/2m)-(ke^{2}/r) and I am assuming e refers to the charge of the electron.
 
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k=1/4pi epsilon0
 
"K" is the constant in Coloumb's Law, just like "G" is a constant in Newton's Law of Gravity.

Numerically, K has a value around 9X10^9 Nm^2/C^2.

As mentioned above by patapat, K can also be represented as:

K=\frac{1}{4\pi\epsilon_0} where \epsilon_0= 8.85X10^-12 and is called the permittivity of free space, which is a fundamental constant of electromagnetism.
 
some of the books use 'k' for representing the quantity '1/4pi*e0'
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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