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?
it depends on how far apart the two charges are.
q*E=F
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 find the magnitude of the net electrostatic force experienced by the Boron nucleus, we need to consider the individual forces between each charged particle and the Boron nucleus. Then, we can calculate the net force by summing up these individual forces using the principles of vector addition.
Let's break down the problem step by step:
Step 1: Calculate the individual electrostatic forces.
- The electrostatic force between charged particles is given by Coulomb's Law: F = k * (q1 * q2)/(r^2), where F is the force, k is the electrostatic constant (8.99 x 10^9 Nm²/C²), q1 and q2 are the charges of the particles, and r is the distance between them.
The Boron nucleus and the Magnesium nucleus both have a positive charge, while the 3e charge on the y-axis has a negative charge. Let's denote the charge on the Boron nucleus as q1, the charge on the Magnesium nucleus as q2, and the charge on the 3e charge as q3.
Step 2: Calculate the distance between these particles.
- The problem states that the point of interest (P) is halfway between the Magnesium nucleus and the 3e charge on the y-axis. To calculate the distance between them, we need to determine the distance between the Magnesium nucleus and the 3e charge and then divide it by 2.
Let's denote the distance between the Magnesium nucleus and the 3e charge as "d". The distance between the point P and the Magnesium nucleus is (d/2).
Step 3: Calculate the net force.
- To find the net force, we need to calculate the individual forces between each charged particle and the Boron nucleus, taking into account the direction of the forces.
Let's denote the force between the Boron nucleus and the Magnesium nucleus as F1, and the force between the Boron nucleus and the 3e charge as F2.
The net force (Fnet) is given by: Fnet = sqrt(F1^2 + F2^2), where sqrt represents the square root.
By calculating Fnet using the values we obtained, we can determine the magnitude of the net electrostatic force the Boron nucleus experiences at the point halfway between the Magnesium nucleus and the 3e charge.