Final answer:
The amount of work required to increase the distance between -6μC and 4μC from 6 cm to 18 cm is approximately 1.8 J (option a).
Therefore, the amount of work required to increase the distance between -6μC and 4μC from 6 cm to 18 cm is approximately 1.8 J (option a).
Step-by-step explanation:
The amount of work required to increase the distance between -6μC and 4μC from 6 cm to 18 cm can be calculated using the formula:
Work = force × distance
The force between two charges can be found using Coulomb's Law:
Force = (k × |q1 × q2|) / r2
Where k is the electrostatic constant (k = 8.99 × 109 N m2/C2), q1 and q2 are the charges, and r is the distance between them.
First, we need to calculate the force at the initial distance:
Force_initial = (8.99 × 109 N m2/C2) × ((6 × 10-6 C) × (4 × 10-6 C)) / (6 × 10-2 m)2
Next, we calculate the force at the final distance:
Force_final = (8.99 × 109 N m2/C2) × ((6 × 10-6 C) × (4 × 10-6 C)) / (18 × 10-2 m)2
Finally, the work done is the difference in forces multiplied by the change in distance:
Work = (Force_final - Force_initial) × (18 × 10-2 m - 6 × 10-2 m)
Simplifying the calculations, we get:
Work ≈ 1.8336 J