3 identical point charges Q are placed at the vertices of equilateral triangle (length of each side is equal to 2m) if Q=60uC, what is the magnitude of Electrostatic force on any one of the charges.
To find the magnitude of the electrostatic force on any one of the charges, we first need to calculate the electric field at the position of each charge due to the other two charges. Then, we can use Coulomb's law to calculate the force.
Step 1: Calculate the electric field at each charge. Since the charges are at the vertices of an equilateral triangle, the electric field at each charge can be found by summing the contributions from the other two charges.
The electric field due to a point charge Q is given by the formula:
E = (k * Q) / r^2
Where:
- E is the electric field
- k is the electrostatic constant (9 × 10^9 N m^2/C^2)
- Q is the charge magnitude
- r is the distance from the charge
For each charge, the distance to the other two charges is the length of the side of the equilateral triangle (2 m).
Thus, the electric field at each charge is:
E = (k * Q) / (2m)^2
Step 2: Calculate the force on one of the charges using Coulomb's Law.
Coulomb's law states that the force between two charges is given by the formula:
F = (k * Q1 * Q2) / r^2
Where:
- F is the electric force
- Q1 and Q2 are the magnitudes of the two charges
- r is the distance between the charges
In this case, since all three charges are identical, Q1 = Q2 = Q.
We need to calculate the force on one charge, so we can take Q1 = Q and Q2 = Q.
The distance between the charges is also the length of the side of the equilateral triangle (2 m).
Thus, the force on one charge due to the other two is:
F = (k * Q * Q) / (2m)^2
Now we can substitute the given values:
Q = 60 μC (1 μC = 10^-6 C)
F = (9 × 10^9 N m^2/C^2) * (60 × 10^-6 C)^2 / (2m)^2
F = (9 × 10^9 N m^2/C^2) * 3.6 × 10^-9 C^2 / 4 m^2
Simplifying the expression:
F = (9 × 3.6 / 4) × (10^9 N m^2/C^2) × (10^-9 C^2)
F = 8.1 N
Therefore, the magnitude of the electrostatic force on any one of the charges is 8.1 N.