A proton is located at x = 1.0 nm, y=0.0nm. and an electron is located at x=0.0nm y=3.0nm. Find the attractive Coulombic force between them. (The value of k is 9.0 * 10^9 N*m^2/C^2)
I found 2.3 x 10^-11 N am I correct?
To find the attractive Coulombic force between a proton and an electron, we can use Coulomb's Law. Coulomb's Law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
F is the force between the particles,
k is the Coulomb's constant (k = 9.0 * 10^9 N*m^2/C^2),
|q1| and |q2| are the magnitudes of the charges of the particles,
and r is the distance between the particles.
In this case, we have a proton and an electron, which have opposite charges. The magnitude of the charge of a proton is |q1| = 1.6 * 10^-19 C, and the magnitude of the charge of an electron is |q2| = 1.6 * 10^-19 C. The distance between them is r = √[(x2 - x1)^2 + (y2 - y1)^2].
Given:
x1 = 1.0 nm, y1 = 0.0 nm (proton location)
x2 = 0.0 nm, y2 = 3.0 nm (electron location)
Calculating the distance:
r = √[(x2 - x1)^2 + (y2 - y1)^2]
r = √[(0.0 - 1.0)^2 + (3.0 - 0.0)^2]
r = √(1 + 9)
r = √10 nm
Substituting the values into Coulomb's Law:
F = (9.0 * 10^9 N*m^2/C^2) * (|q1| * |q2|) / r^2
F = (9.0 * 10^9 N*m^2/C^2) * (1.6 * 10^-19 C * 1.6 * 10^-19 C) / (10 nm)^2
Calculating the force:
F = (9.0 * 10^9 N*m^2/C^2) * (2.56 * 10^-38 C^2) / (10^-18 m^2)
F = 2.304 N
So the attractive Coulombic force between the proton and electron is 2.304 N. Therefore, your answer of 2.3 x 10^-11 N is incorrect.