Four equal charges 2.0×10^(-6) coulomb each are fixed at the four corn...
Four equal charges are fixed at the four corners of a square, and we need to find the Coulomb force experienced by one of the charges due to the rest three. Let's break down the problem step by step.
Step 1: Identifying the given information
- Charges: Four equal charges, each with a magnitude of 2.0×10^(-6) Coulombs.
- Geometry: The charges are fixed at the four corners of a square.
- Side length: The side length of the square is given as 5 cm.
Step 2: Understanding the Coulomb force
The Coulomb force is the electrostatic force of attraction or repulsion between two charged objects. It is given by Coulomb's law:
F = k * (q1 * q2) / r^2
where F is the force, k is the electrostatic constant (9 × 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Step 3: Determining the distances
Since the charges are fixed at the corners of a square, we can determine the distances between them. The diagonal of a square can be calculated using the Pythagorean theorem:
d = √(s^2 + s^2) = √(2s^2)
where d is the diagonal length and s is the side length of the square. In this case, s = 5 cm, so
d = √(2 * 5^2) = √50 = 5√2 cm
The distance between the charges along the sides of the square is equal to the side length, which is 5 cm.
Step 4: Calculating the Coulomb forces
The force experienced by one charge due to the other charges can be calculated using Coulomb's law. Let's consider one of the charges and calculate the forces due to the other three charges.
Force due to the charge opposite to it:
The charge opposite to the chosen charge is located at a distance of 5√2 cm. Using Coulomb's law:
F1 = (9 × 10^9 N m^2/C^2) * ((2.0×10^(-6) C)^2) / ((5√2 cm)^2)
Simplifying the equation:
F1 = (9 × 10^9 N m^2/C^2) * (4.0×10^(-12) C^2) / (50 cm^2)
Force due to the charges adjacent to it:
The charges adjacent to the chosen charge are located at a distance of 5 cm. Using Coulomb's law:
F2 = (9 × 10^9 N m^2/C^2) * ((2.0×10^(-6) C)^2) / ((5 cm)^2)
Simplifying the equation:
F2 = (9 × 10^9 N m^2/C^2) * (4.0×10^(-12) C^2) / (25 cm^2)
Step 5: Summing up the forces
To find the total force experienced by the chosen charge, we need to sum
Four equal charges 2.0×10^(-6) coulomb each are fixed at the four corn...
Is the answer 36 N?
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