A test charge of +2 x 10^-7 C is located 5 cm to the right of a charge of +1 x 10^-6 C and 10 cm to the left of a charge of -1x10^-6 C. The three charges lie on a straight line. Find the force on the test charge? with solution

To find the force on the test charge, we need to calculate the individual forces exerted by each charge and then sum them up.

Step 1: Determine the distance between the test charge and each of the other charges.
- Test charge to the +1 x 10^-6 C charge: 5 cm (to the right)
- Test charge to the -1 x 10^-6 C charge: 10 cm (to the left)

Step 2: Calculate the force between the test charge and each of the other charges using Coulomb's Law:
The force between two charges can be calculated using the formula:
F = k * (|q1| * |q2|) / r^2

where:
F = Force between the charges
k = Coulomb's constant = 9 x 10^9 Nm^2/C^2
q1, q2 = Magnitudes of the charges
r = Distance between the charges

Using this formula, we can calculate the individual forces:

Force exerted by the +1 x 10^-6 C charge:
F1 = k * |(+2 x 10^-7 C)| * |(+1 x 10^-6 C)| / (0.05 m)^2

Force exerted by the -1 x 10^-6 C charge:
F2 = k * |(+2 x 10^-7 C)| * |(-1 x 10^-6 C)| / (0.10 m)^2

Step 3: Calculate the net force on the test charge:
The net force is the vector sum of the forces exerted by each charge.
Since the charges are arranged in a straight line, the forces are in opposite directions. Therefore, the net force is the difference between the magnitudes of the two individual forces:

Net Force = |F1| - |F2|

Substituting the values and using the equation above, we can calculate the net force on the test charge.