Three charges q1(-1.0×10²) q1(-2×10²) and q3(-3×10²) are arranged on the apex of an equilateral triangle of sides 5cm. Find the resultant force on the charge q1
To find the resultant force on charge q1, we need to calculate the individual forces due to q2 and q3 and then find their vector sum.
The force between two charges can be found using Coulomb's Law:
F = (k * |q1| * |q2|) / r^2
where F is the force, k is the Coulomb constant (8.99 x 10^9 N*m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
Let's find the force between q1 and q2 first.
- Magnitude of q1: |q1| = 1.0 x 10^-2 C
- Magnitude of q2: |q2| = 2.0 x 10^-2 C
- Distance between q1 and q2: r12 = length of the side of the equilateral triangle = 5 cm = 0.05 m
Now, we can calculate the force between q1 and q2:
F12 = (k * |q1| * |q2|) / r12^2
= (8.99 x 10^9 N*m^2/C^2 * 1.0 x 10^-2 C * 2.0 x 10^-2 C) / (0.05 m)^2
Calculating this provides the magnitude of the force between q1 and q2.
Similarly, we can find the forces between q1 and q3 and between q2 and q3 using the same steps.
Once we have the magnitudes and directions of all three forces, we can use vector addition to find the resultant force on q1. The vector sum of the three forces will give us the magnitude and direction of the resultant force.
Let's calculate the individual forces and then find the resultant force on q1.