A charge of 4.00 mC is placed at each corner of a square 1.05 m on a side. Determine the magnitude and direction of the force on each charge.

q1, q2, q3,q4 –from the lower left corner – counterclockwise.

Origin of the coordinate system is at the corner where q1 is located.

F12=k•q1•q2/a² =
=9•10^9•4•10^-3•4•10^-3/1.05²=
= 130612 N
F12x=0, F12y= - 130612 N.

F13=k•q1•q3/ (a√2)² =
=9•10^9•4•10^-3•4•10^-3/1.05²•1.41=
= 92633N
F13x=F13y= - 92633 •cos45= - 65491 N.

F14=k•q1•q4/a² =
=9•10^9•4•10^-3•4•10^-3/1.05²=
= 130612 N
F14x= - 130612 N, F14y =0 N.

F1x= F12x+ F13x +F14x =0 - 65491- 130612 = - 196103 N,
F1y= F12y+ F13y +F14y = - 130612 – 65491 -0= - 196103 N.
F1=sqrt(F1x² + F1y²) =sqrt(196103² + 196103 ²) =277331 N.
tanα = F1y/ F1x= 1
=> along the diagonal of the square, away from each charge.
The same force acts on each charge

To determine the magnitude and direction of the force on each charge, we can use Coulomb's Law, which states that the magnitude of the electrostatic 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.

Let's label the charges at the corners of the square as Q1, Q2, Q3, and Q4.

Since all the charges are the same and equal to 4.00 mC, the magnitude of each charge is q = 4.00 mC.

The distance between adjacent charges is the length of one side of the square, which is 1.05 m.

Using Coulomb's Law, the magnitude of the force between any two charges is given by:

F = (k * |q1 * q2|) / r^2,

where F is the magnitude of the force, k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.

Let's calculate the forces acting on each charge:

1. The force on Q1 due to Q2:
F1-2 = (9 × 10^9 Nm^2/C^2 * |(4.00 × 10^(-3) C) * (4.00 × 10^(-3) C)|) / (1.05 m)^2

2. The force on Q1 due to Q3:
F1-3 = (9 × 10^9 Nm^2/C^2 * |(4.00 × 10^(-3) C) * (4.00 × 10^(-3) C)|) / (1.05 m)^2

3. The force on Q1 due to Q4:
F1-4 = (9 × 10^9 Nm^2/C^2 * |(4.00 × 10^(-3) C) * (4.00 × 10^(-3) C)|) / (1.05 m)^2

The magnitude of the force on Q1 is given by the vector sum of the forces F1-2, F1-3, and F1-4. The direction of the force can be determined by the angle between the forces.

Repeat the same calculations for the forces acting on Q2, Q3, and Q4 due to the other charges.

This procedure will give you the magnitude and direction of the force on each charge.

To determine the magnitude and direction of the force on each charge, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Step 1: Calculate the distance between the charges.
The distance between the charges can be calculated using the Pythagorean theorem, as the charges are placed at the corners of a square.

The diagonal length of the square can be calculated as:
diagonal length = side length * √2 = 1.05 m * √2 = 1.48 m

Step 2: Calculate the force between two charges using Coulomb's Law.
Coulomb's Law states that F = k * (q1 * q2) / r^2, where F is the force, k is the electrostatic constant (9.0 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

Using this formula, we can calculate the force between two charges:
F = (9.0 × 10^9 N m^2/C^2) * (4.00 mC * 4.00 mC) / (1.48 m)^2

Calculating this gives us:
F = 2.96 × 10^4 N

Step 3: Determine the direction of the force.
The force will be repulsive as the charges are of the same sign (positive). Therefore, the force will act away from each charge.

Step 4: Repeat steps 2 and 3 for each pair of charges.
In this case, we have four charges arranged at the corners of the square. We need to repeat steps 2 and 3 for each pair of charges.

For the top-left charge:
Magnitude of the force = 2.96 × 10^4 N
Direction of the force = Away from the charge

For the top-right charge:
Magnitude of the force = 2.96 × 10^4 N
Direction of the force = Away from the charge

For the bottom-left charge:
Magnitude of the force = 2.96 × 10^4 N
Direction of the force = Away from the charge

For the bottom-right charge:
Magnitude of the force = 2.96 × 10^4 N
Direction of the force = Away from the charge

So, the magnitude of the force on each charge is 2.96 × 10^4 N, and the direction of the force is away from each charge.