Three identical point charges A, B, and C are located in the shape of an equilateral triangle with sides of length 15 cm. What is the net force on B if each charge has a magnitude of −5.0 × 10−3 C?
To determine the net force on charge B, we need to calculate the individual forces between B and charges A and C using Coulomb's Law, and then find the vector sum of these forces.
Coulomb's Law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. The formula for Coulomb's Law is as follows:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the magnitude of the force between the charges.
- k is Coulomb's constant (8.99 × 10^9 Nm^2/C^2).
- |q1| and |q2| are the magnitudes of the charges.
- r is the distance between the charges.
In this case, charges A, B, and C all have the same magnitude, which is -5.0 × 10^-3 C, and the distance between them is equal to the side length of the equilateral triangle, which is 15 cm.
1. Calculating the force between B and A:
F_AB = k * (|qA| * |qB|) / r^2
= (8.99 × 10^9 Nm^2/C^2) * (5.0 × 10^-3 C) * (5.0 × 10^-3 C) / (15 cm)^2
2. Calculating the force between B and C:
F_BC = k * (|qC| * |qB|) / r^2
= (8.99 × 10^9 Nm^2/C^2) * (5.0 × 10^-3 C) * (5.0 × 10^-3 C) / (15 cm)^2
Now, the net force on B is the vector sum of these forces.
3. Finding the vector sum of forces F_AB and F_BC:
- Since the equilateral triangle is symmetrical, the forces F_AB and F_BC have the same magnitude and act along the lines joining the corresponding charges.
- The angle between the vectors F_AB and F_BC is 120 degrees, representing the angles of an equilateral triangle.
- To find the net force, we can use vector addition by adding the forces as vectors:
F_net = sqrt((F_AB + F_BC)^2 + 2 * F_AB * F_BC * cos(120 degrees))
Once you calculate the value of F_net, this will represent the net force on charge B.