An electron and a proton are separated by 2.0 nm. (a) What is the magnitude of the force on the electron? (b) What is the net force on the system?
(a) Well, let's see here. The electron and the proton, huh? Talk about a dynamic duo! Now, the magnitude of the force on the electron can be determined using the formula for electrical force: F = k * (q1 * q2) / r^2, where k is Coulomb's constant, q1 and q2 are the charges of the electron and proton respectively, and r is the separation distance between them.
So, plugging in the values, we have F = (9 * 10^9 N m^2/C^2) * ((1.6 * 10^-19 C) * (1.6 * 10^-19 C)) / (2 * 10^-9 m)^2. Crunching the numbers, the magnitude of the force on the electron is approximately 9.12 * 10^-8 N.
(b) Now, the net force on the system would be the absolute value of this force because these two charges would attract each other due to their opposite signs. So, the net force on the system is approximately 9.12 * 10^-8 N. Remember, teamwork makes the dream work!
To find the magnitude of the force between an electron and a proton, 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.
(a) To find the magnitude of the force on the electron:
The charge of an electron is -1.6 x 10^-19 Coulombs (C), and the charge of a proton is +1.6 x 10^-19 C.
The distance between them is 2.0 nm, which can be converted to meters by multiplying by 10^-9:
Distance (r) = 2.0 nm x 10^-9 = 2.0 x 10^-9 m
The force equation is given by:
F = (k * |q1 * q2|) / r^2
Where:
F is the force,
k is Coulomb's constant, approximately 9 x 10^9 Nm^2/C^2,
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
Substituting the values into the equation:
F = (9 x 10^9) * (|-1.6 x 10^-19 C| * |1.6 x 10^-19 C|) / (2.0 x 10^-9 m)^2
Calculating this expression will give the magnitude of the force on the electron.
(b) The net force on the system is the vector sum of the forces acting on both particles. Since the charges are equal in magnitude but opposite in sign, the forces will have the same magnitude but opposite directions. Therefore, the net force on the system will be zero, as the forces cancel each other out.
To find the magnitude of the force on the electron and the net force on the system, we can use Coulomb's law, which relates the force between two charged particles to the charge and distance between them.
Coulomb's law equation is:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the two charged particles,
k is the electrostatic constant (k = 9.0 x 10^9 N*m^2/C^2),
|q1| and |q2| are the magnitudes of the charges of the two particles, and
r is the distance between the charges.
(a) Magnitude of the force on the electron:
In this case, the electron and proton have opposite charges, so |q1| = |q2| = e, where e is the elementary charge (e = 1.6 x 10^-19 C).
The distance between them is given as r = 2.0 nm = 2.0 x 10^-9 m.
Substituting these values in the Coulomb's law equation:
F = (k * |q1 * q2|) / r^2
= (9.0 x 10^9 N*m^2/C^2 * (1.6 x 10^-19 C)^2) / (2.0 x 10^-9 m)^2
Calculating this expression will give you the magnitude of the force on the electron.
(b) Net force on the system:
The net force on the system will depend on the magnitudes of the charges and the distance between them. Since the electron and proton have opposite charges, the net force on the system will be zero. This is due to the principle of electrostatic equilibrium, where the forces between charged particles cancel out in a stable system.
Therefore, the net force on the system is 0 N.
a) Use Coulomb's Law
F = k e^2/R^2
b) zero, unless there is an external electric or magnetic field. The forces of the electron and proton on each other cancel out.