How much work is needed to move a charge of -4 micro C to a point 50m from a charge 30 micro C
To calculate the work needed to move a charge from one point to another due to an electric field, you can use the formula:
Work (W) = Charge (Q) × Electric Potential Difference (ΔV)
First, let's calculate the electric potential difference (ΔV) between the two points:
ΔV = k × (Q1 / r1 - Q2 / r2)
Where:
- k is the electrostatic constant (9 × 10^9 Nm^2/C^2)
- Q1 and Q2 are the charges
- r1 and r2 are the distances from the charges to the point of interest
Given:
- Q1 = -4 µC (negative sign indicates a negative charge)
- Q2 = 30 µC
- r1 = 50 m
- r2 = 0 m (since we assume the charge is located at that point)
Let's calculate ΔV:
ΔV = (9 × 10^9 Nm^2/C^2) × [(-4 × 10^-6 C) / (50 m) - (30 × 10^-6 C) / (0 m)]
Note: The term (30 × 10^-6 C) / (0 m) can be ignored since we cannot divide by zero.
ΔV = (9 × 10^9 Nm^2/C^2) × [(-4 × 10^-6 C) / (50 m)]
ΔV = - 0.72 J (Joules)
Now that we have the electric potential difference, we can calculate the work needed to move the charge:
Work (W) = (Charge) × (Electric Potential Difference)
W = (-4 × 10^-6 C) × (-0.72 J)
W = 2.88 × 10^-6 J (Joules)
Therefore, the work needed to move a charge of -4 µC to a point 50 m from a charge of 30 µC is approximately 2.88 × 10^-6 Joules.