The force of interaction between two charges q1=6uC and q2=2uC is 12N. If charge q=-2uC is added to each of the charges then the new force of interaction is

zero

To find the new force of interaction after charge q = -2uC is added to each of the charges, we need to consider the principle of superposition.

1. Original force of interaction:
Given that the force of interaction between q1 and q2 is 12N, we know that the original force can be represented as:

F1 = k * (q1 * q2) / r^2

where k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2) and r is the distance between the charges.

2. New charges after adding q = -2uC:
After adding q = -2uC to each of the charges, the new charges are:
q1' = q1 + q = 6uC - 2uC = 4uC
q2' = q2 + q = 2uC - 2uC = 0uC

3. New force of interaction:
Using the principle of superposition, the new force of interaction can be calculated as:

F2 = k * (q1' * q2') / r^2

Substituting the values:

F2 = (9 x 10^9 Nm^2/C^2) * (4 x 10^-6 C) * (0 C) / (r^2)
= 0 N

Therefore, the new force of interaction after adding q = -2uC to each of the charges is 0N.

To find the new force of interaction after adding a charge to each of the charges, we need to calculate the new values of the charges and plug them into the formula for the force of interaction.

1. Start with the given charges:
q1 = 6μC
q2 = 2μC

2. Add the charge q to each of the charges:
New q1 = q1 + q = 6μC + (-2μC) = 4μC
New q2 = q2 + q = 2μC + (-2μC) = 0μC

3. Calculate the new force of interaction:
F = (k * |q1 * q2|) / r^2
where k is the Coulomb's constant (k ≈ 9 × 10^9 Nm^2/C^2) and r is the distance between the charges.

Since q2 is now 0, the new force of interaction becomes:
F = (k * |q1 * q2|) / r^2 = (k * |4μC * 0μC|) / r^2 = 0N

Thus, the new force of interaction after adding a charge of -2μC to each of the charges is 0N. Explanation: When a charge of -2μC is added to each of the charges, the resulting charges cancel out each other's effect, resulting in a net force of 0N.

F = k q1 q2 /d^2

q1*q2 = 6*2 = 12

new q1*q2 = 8*4 = 32

so
(32/12)12N = 32 N