if a 3e charge is at the origin and a magnesium nucleus is 3 cm from the originin the x-axis direction.what is the magnitude of the net electrostatic force a Boron nucleus would experience at the point half way between magnesium nucleus and 3e charge on the y-axis in N
To calculate the magnitude of the net electrostatic force, we need to consider the individual forces between the given charges and the Boron nucleus at the specific point. The net electrostatic force will be the vector sum of these individual forces.
Let's break down the problem step by step:
Step 1: Determine the value of the charge for each particle:
- The charge of the 3e charge at the origin is 3 * e (where e is the elementary charge, 1.602 x 10^-19 C).
- The charge of the magnesium nucleus is +2e (positive because it has two protons).
Step 2: Calculate the distance between the Boron nucleus and the magnesium nucleus.
- The distance from the origin to the point half-way between the magnesium nucleus and the 3e charge on the y-axis is 3 cm.
- Since the magnesium nucleus is 3 cm from the origin in the x-axis direction, the distance between the Boron nucleus and the magnesium nucleus can be found using the Pythagorean theorem.
- The distance between them is sqrt((3^2) + (1.5^2)) = sqrt(9 + 2.25) = sqrt(11.25) = 3.355 cm.
Step 3: Use Coulomb's law to calculate the magnitude of each individual force:
- Coulomb's law states that the magnitude of the electrostatic force between two charged particles is given by F = k * (|q1| * |q2|) / r^2, where k is the electrostatic constant (k = 8.99 x 10^9 N * m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
- The force between the Boron nucleus and the 3e charge is F1 = (k * (|3 * e| * |e|)) / (3.355e-2)^2.
- The force between the Boron nucleus and the magnesium nucleus is F2 = (k * (|+2e| * |e|)) / (3.355e-2)^2.
Step 4: Calculate the net electrostatic force:
- The net force is given by the vector sum of the individual forces: F_net = sqrt(F1^2 + F2^2).
Now, you can plug in the values into these equations and calculate the magnitude of the net electrostatic force.