What is the magnitude of the net electrostatic force a Boron nucleus would experience at the point halfway between the Magnesium nucleus and the 3e charge on the y axis in N?
q₁ = 3 e,
q₂ = 12e,
q₃ = 5e
The electric field at the midpoint is
E= kq₂/(x/2)²- kq₁/(x/2)²=
=k(12e-3e)/(x/2)² =k36e/x² (directed to the 3e charge)
F= q₃E=k36e•5e/x²=
=k•180e/x²,
where
k =9•10⁹ N•m²/C²,
e =1.6•10⁻¹⁹ C,
x is the distance between 3e and 12e
To determine the magnitude of the net electrostatic force a Boron nucleus would experience at the point halfway between the Magnesium nucleus and the 3e charge on the y-axis, we can use Coulomb's law and the principle of superposition.
Coulomb's law states that the electrostatic 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.
1. First, we need to calculate the individual electrostatic forces between the Boron nucleus and the Magnesium nucleus, as well as between the Boron nucleus and the 3e charge.
2. To calculate the electrostatic force between two charged particles, we can use the following formula:
F = (k * |q1 * q2|) / r^2,
where F is the electrostatic force, k is the electrostatic constant (9 × 10^9 N·m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.
3. The net electrostatic force is the vector sum of the electrostatic forces acting on the Boron nucleus. Since we are interested only in the magnitude, we can ignore the directions of the forces.
Fnet = sqrt(F1^2 + F2^2),
where F1 and F2 are the electrostatic forces between the Boron nucleus and the Magnesium nucleus, and between the Boron nucleus and the 3e charge, respectively.
4. Let's break down the steps to calculate the individual electrostatic forces:
a. Calculate the distance between the Magnesium nucleus and the halfway point between the Magnesium nucleus and the 3e charge on the y-axis.
b. Calculate the distance between the Boron nucleus and the halfway point.
c. Calculate the distance between the 3e charge on the y-axis and the halfway point.
d. Use Coulomb's law to calculate the electrostatic force between the Magnesium nucleus and the halfway point.
e. Use Coulomb's law to calculate the electrostatic force between the Boron nucleus and the halfway point.
f. Add the magnitudes of the forces using the principle of superposition to obtain the net force.
By following these steps, you will be able to calculate the magnitude of the net electrostatic force with the given information.