Four equal point charges, +3micro coulomb, are placed at the four corners of a square that is 40cm on a side. Find the force on any one of the charges.
Give mr solution
F≈0.97N
To find the force on any one of the charges, you can use Coulomb's law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Step 1: Calculate the electric force between two charges
The electric force (F) between two charges (q1 and q2) can be calculated using the formula: F = k * (|q1| * |q2|) / r^2. Here, k is the electrostatic constant, |q1| and |q2| are the magnitudes of the charges, and r is the distance between them.
Step 2: Calculate the force on one charge due to the other charges
In this case, we have four charges at the corners of a square. The force on any one of the charges will be the sum of the forces due to the other three charges.
Step 3: Calculate the magnitude and direction of the force
Since the charges are all equal, the magnitude of the force on any one of the charges will be the same. To find the direction, consider the symmetry of the square configuration. The forces between the opposite charges (diagonally across the square) will cancel each other out, resulting in a net force along the lines connecting adjacent charges.
Now let's calculate the force on any one of the charges:
Step 1: Calculate the force between two charges
Given:
Charge (q1) = Charge (q2) = +3 microcoulombs = 3 × 10^-6 C
Distance (r) between charges = length of the side of the square = 40 cm = 0.4 m
Using Coulomb's law, the electric force between two charges is:
F = k * (|q1| * |q2|) / r^2
Substituting the values:
F = (9 × 10^9 N m^2/C^2) * ((3 × 10^-6 C) * (3 × 10^-6 C)) / (0.4 m)^2
Simplifying the equation:
F = (9 × 10^9 N m^2/C^2) * 9 × 10^-12 C^2 / 0.16 m^2
F = (9 × 9) × 10^-3 N
F = 81 × 10^-3 N
F = 81 mN (millinewtons)
Now let's calculate the force on any one of the charges due to the other three charges:
Step 2: Calculate the total force on one charge due to the other charges
Since we have four charges, the total force on any one of the charges will be the sum of the forces due to the other three charges.
Since the force between each pair of charges is the same and they are arranged at the corners of a square, the magnitude of the total force on any one of the charges will be:
Total force = 3 × Force between two charges
Total force = 3 × 81 mN
Total force = 243 mN
Therefore, the force on any one of the charges is 243 millinewtons.