Electric Force Calculation

To find the force experienced by the charge at x = 2cm, we need to use Coulomb's law. Coulomb's law states that the electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Coulomb's Law:
The electric force (F) between two charges (q1 and q2) is given by the formula:

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

Where:
- F is the electric force
- k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2)
- q1 and q2 are the charges
- r is the distance between the charges

Calculating the Force:

In this case, we have equal charges of 20mc (20 × 10^-6 C) placed at x = 2cm, 4cm, 8cm, and 16cm on the x-axis. We need to find the force experienced by the charge at x = 2cm.

Step 1: Convert the distance from centimeters to meters:
- x = 2cm = 2 × 10^-2 m

Step 2: Calculate the distance between the charges:
- The distance between the charges at x = 2cm and x = 2cm is 0cm, so we can exclude it from the calculation.

- The distance between the charge at x = 2cm and x = 4cm is 4cm - 2cm = 2cm = 2 × 10^-2 m.

- The distance between the charge at x = 2cm and x = 8cm is 8cm - 2cm = 6cm = 6 × 10^-2 m.

- The distance between the charge at x = 2cm and x = 16cm is 16cm - 2cm = 14cm = 14 × 10^-2 m.

Step 3: Calculate the force between the charges:
- The force between the charges at x = 2cm and x = 2cm is 0, as they are the same charge.

- The force between the charges at x = 2cm and x = 4cm is given by the formula:
F = (9 × 10^9 Nm^2/C^2) * [(20 × 10^-6 C) * (20 × 10^-6 C)] / [(2 × 10^-2 m)^2]

- The force between the charges at x = 2cm and x = 8cm is given by the formula:
F = (9 × 10^9 Nm^2/C^2) * [(20 × 10^-6 C) * (20 × 10^-6 C)] / [(6 × 10^-2 m)^2]

- The force between the charges at x = 2cm and x = 16cm is given by the formula:
F = (9 × 10^9 Nm^2/C^2) * [(20 × 10^-6 C) * (20 × 10^-6 C)] / [(14 × 10^-2 m)^2