Question

A test charge q = 9 nC moves from point A to point B in the electric field created by a charge Q = 4 μC. The distance from point A to the charge Q is 20 cm, whereas the distance from point B to the charge Q is 40 cm. Calculate the work done in moving the charge q from point A to point B. Round your answer to the nearest microjoule.

Answer 1

The work done in moving the charge q from point A to point B is approximately 1.62 microjoules.

Step-by-step explanation:

To calculate the work done in moving the charge q from point A to point B in the electric field created by charge Q, we can use the formula:

Work = q * (ΔV)

Where:

• - q is the test charge (9 nC)
• - ΔV is the change in electric potential between point A and point B

To find the change in electric potential, we can use the formula:

ΔV = (k * |Q|) * ((1 / rA) - (1 / rB))

Where:

• - k is the electrostatic constant (k = 9 × 10⁹ N m²/C²)
• - |Q| is the magnitude of charge Q (4 μC)
• - rA is the distance from point A to charge Q (20 cm = 0.2 m)
• - rB is the distance from point B to charge Q (40 cm = 0.4 m)

Now let's substitute the values into the formulas and calculate the work done:

1. Calculate the change in electric potential:

• ΔV = (9 × 10⁹ N m²/C²) * (4 × 10^-6 C) * ((1 / 0.2 m) - (1 / 0.4 m))
• ΔV = (9 × 10⁹ N m²/C²) * (4 × 10^-6 C) * (5 C/m)
• ΔV = 180 × 10³ J/C

2. Calculate the work done:

• Work = (9 × 10⁻⁹ C) * (180 × 10³ J/C)
• Work = 1620 × 10⁻⁶ J
• Work ≈ 1.62 μJ (rounded to the nearest microjoule)

Therefore, the work done in moving the charge q from point A to point B is approximately 1.62 microjoules.