Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of anequilateral triangle. The magnitude of each charge is 5 microCouloumbs, and the lengths of the sides of the triangle are 3.0cm.Calculate the magnitude of the net force that each charge experiences.
250N
To calculate the magnitude of the net force that each charge experiences, we need to apply Coulomb's Law, which states that the 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.
In this case, we have three charges forming an equilateral triangle. Let's assume that the positive charges are labeled as A and B, and the negative charge is labeled as C.
The formula for Coulomb's Law is:
F = k * |q1 * q2| / r^2
Where:
F is the magnitude of the force between the charges,
k is Coulomb's constant, approximately 8.99 × 10^9 N·m^2/C^2,
q1 and q2 are the magnitudes of the two charges, and
r is the distance between the charges.
Since the charges are fixed at the corners of an equilateral triangle, the distance between any two charges will be the length of one side of the triangle, which is 3.0 cm or 0.03 m.
Now, let's calculate the force experienced by each charge:
1. The force on charge A:
F_A = k * |q1 * q2| / r^2
= 8.99 × 10^9 N·m^2/C^2 * |5 × 10^(-6) C * 5 × 10^(-6) C| / (0.03 m)^2
2. The force on charge B:
F_B = k * |q1 * q2| / r^2
= 8.99 × 10^9 N·m^2/C^2 * |5 × 10^(-6) C * 5 × 10^(-6) C| / (0.03 m)^2
3. The force on charge C:
F_C = k * |q1 * q2| / r^2
= 8.99 × 10^9 N·m^2/C^2 * |-5 × 10^(-6) C * 5 × 10^(-6) C| / (0.03 m)^2
Notice that the force on charge C is negative because it is attracted to the positive charges.
Now you can calculate the values of F_A, F_B, and F_C using this formula and the given values.