if 3e charge is at the origin and magnesium nucleus is 3cm fom thr origin in the x-axis. what is the magnitude of the net electrostatic force a Boron nucleus would experience at a point half way between magnesium nucleus and 3e.
To find the magnitude of the net electrostatic force that a Boron nucleus would experience at a point halfway between the magnesium nucleus and 3e, we can use Coulomb's Law.
Coulomb's Law states that the magnitude of the electrostatic force between two charged objects 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 electrostatic force, k is the Coulomb's constant (approximately 9 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the objects, and r is the distance between the objects.
In this case, we have:
Charge of 3e = 3e = 3 * 1.6 x 10^-19 C
Charge of magnesium nucleus = 0 (since it is neutral)
Charge of Boron nucleus = +5e = 5 * 1.6 x 10^-19 C
Distance between the magnesium nucleus and the Boron nucleus = 3 cm = 0.03 m
Since the magnesium nucleus is neutral, the electrostatic force between the magnesium nucleus and the Boron nucleus will be zero. Hence, we only need to find the electrostatic force between the 3e charge and the Boron nucleus.
Substituting the values in Coulomb's Law equation, we have:
F = (9 x 10^9 Nm^2/C^2) * ((3e) * (+5e)) / (0.03)^2
Now, let's calculate the charge of 3e:
Charge of 3e = 3 * 1.6 x 10^-19 C = 4.8 x 10^-19 C
Substituting the values into the equation, we have:
F = (9 x 10^9 Nm^2/C^2) * ((4.8 x 10^-19 C) * (5 * 1.6 x 10^-19 C)) / (0.03)^2
Simplifying the equation further, we get:
F = (9 x 10^9 Nm^2/C^2) * (4.8 x 10^-19 C * 8 x 10^-19 C) / 0.0009
F = (9 x 10^9 Nm^2/C^2) * (38.4 x 10^-38 C^2) / 0.0009
Now, multiplying and dividing the values, we get:
F = (9 x 10^9 Nm^2/C^2) * (38.4 / 0.0009) x 10^-38 N
F = (9 x 10^9 Nm^2/C^2) * 42.6667 x 10^-38 N
F ≈ 383,999,973.7 x 10^-29 N
The magnitude of the net electrostatic force that the Boron nucleus would experience at a point halfway between the magnesium nucleus and 3e is approximately 3.840 x 10^-16 N.