To calculate the magnitude and direction of the electric force on each charge at the corners of the square, we can use Coulomb's Law. Coulomb's Law states that the electric 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.
First, let's calculate the magnitude of the electric force on each corner charge.
Given:
- Charge of each corner = -1.0x10^-6 C
- Side length of the square = 2.0 cm
Step 1: Convert the side length from centimeters to meters.
1 meter = 100 centimeters
So, 2.0 cm = 2.0 / 100 = 0.02 meters
Step 2: Calculate the distance between the corner charges.
The distance between opposite corners of the square is equal to the length of its diagonal. In this case, the diagonal is equal to the side length times the square root of 2.
Diagonal of the square = 0.02 * √2 meters
Step 3: Calculate the magnitude of the electric force.
Using Coulomb's Law formula:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the electric force,
k is the Coulomb's 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 calculate the magnitude of the electric force on each corner charge at one of the corners of the square (the other corners will have the same magnitude of force):
F = (8.99 x 10^9 N m^2/C^2) * (|-1.0x10^-6 C| * |-1.0x10^-6 C|) / (0.02 * √2 m)^2
Calculating this, we get:
F ≈ 2.03 x 10^-2 N (rounded to two decimal places)
Since all the corner charges are of the same magnitude (-1.0x10^-6 C) and at the same distance from each other, the magnitude of the electric force on each corner charge will also be approximately 2.03 x 10^-2 N, pointing inwards towards the center of the square.
Now, let's consider the fifth charge placed in the center of the square. The magnitude and direction of the force on this charge will be determined by the other corner charges.
Since the corner charges are negatively charged and the fifth charge is placed in their midst, it will experience an attractive force in the direction towards each corner charge. The magnitude of the force on the fifth charge will be four times the magnitude of the force on each corner charge, since there are four corner charges.
Therefore, the magnitude of the force on the fifth charge will be approximately 4 * 2.03 x 10^-2 N, which simplifies to approximately 8.12 x 10^-2 N (rounded to two decimal places).
The sign of the fifth charge will affect the direction of the force on it. If the fifth charge is negatively charged, it will experience an attractive force towards each corner charge. If the fifth charge is positively charged, it will experience a repulsive force away from each corner charge. However, the magnitude of the force on the fifth charge will remain the same regardless of its sign.