The Superpostion Principle:
Three point charges q1, q2 and q3 like along the x-axis at x=0, x=3.0cm and x=5.0cm, respectively. calculate the magnitude and direction of the electric force on each of the three point charges when q1 = +6.0 microcoulombs q2= +1.5 microcoulombs and q2= -2.0 micro coulombs.
I got the total force to be 47 N but I'm not sure if that is right and I believe I'm missing some answers.
To calculate the magnitude and direction of the electric force on each of the three point charges, you can apply the principle of superposition. This principle states that the total electric force acting on a charge is the vector sum of the individual forces due to each of the other charges.
Step 1: Calculate the electric force on q1 due to q2 and q3.
- The electric force between two charges can be calculated using Coulomb's Law: F = k*q1*q2/r^2, where k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.
- The force on q1 due to q2 is F12 = k*q1*q2/r12^2, where r12 is the distance between q1 and q2 (3.0 cm = 0.03 m).
- The force on q1 due to q3 is F13 = k*q1*q3/r13^2, where r13 is the distance between q1 and q3 (5.0 cm = 0.05 m).
Step 2: Calculate the electric force on q2 due to q1 and q3.
- The force on q2 due to q1 is F21 = k*q2*q1/r21^2, but since q1 and q2 are the same charges, the force will have the same magnitude but opposite direction as F12.
- The force on q2 due to q3 is F23 = k*q2*q3/r23^2, where r23 is the distance between q2 and q3 (2.0 cm = 0.02 m).
Step 3: Calculate the electric force on q3 due to q1 and q2.
- The force on q3 due to q1 is F31 = k*q3*q1/r31^2, but since q1 and q3 are opposite charges, the force will have the same magnitude but opposite direction as F13.
- The force on q3 due to q2 is F32 = k*q3*q2/r32^2, but since q2 and q3 are the opposite charges, the force will have the same magnitude but opposite direction as F23.
Step 4: Calculate the magnitude and direction of the total electric force on each charge.
- The total force on each charge is the vector sum of the forces acting on it.
- The magnitude of the total force on each charge can be calculated by summing the magnitudes of the individual forces.
- The direction of the total force can be determined by considering the directions of the individual forces and applying vector addition.
Calculations:
- F12 = (8.99 x 10^9 Nm^2/C^2) * (6.0 x 10^-6 C) * (1.5 x 10^-6 C) / (0.03 m)^2
- F13 = (8.99 x 10^9 Nm^2/C^2) * (6.0 x 10^-6 C) * (-2.0 x 10^-6 C) / (0.05 m)^2
- F21 = -F12 (opposite direction)
- F23 = (8.99 x 10^9 Nm^2/C^2) * (1.5 x 10^-6 C) * (-2.0 x 10^-6 C) / (0.02 m)^2
- F31 = -F13 (opposite direction)
- F32 = -F23 (opposite direction)
Magnitude and direction of the forces:
- F12 = 180 N (in the positive x-direction)
- F13 = -215.28 N (in the negative x-direction)
- F21 = -180 N (in the negative x-direction)
- F23 = -675 N (in the negative x-direction)
- F31 = -215.28 N (in the positive x-direction)
- F32 = 675 N (in the positive x-direction)
Note: To calculate the total force, you need to sum the forces acting on each charge individually. Simply adding magnitudes may lead to incorrect results.
Therefore, the total force on q1 is the vector sum of F12 and F13, the total force on q2 is the vector sum of F21 and F23, and the total force on q3 is the vector sum of F31 and F32.