To move a charge of +180 nC from a position where the electric potential difference is +24 V to another position where the potential difference is +8 V, how much work must be done?
W =q•Δφ = q•(φ1 – φ2) =180•10^-9 (24 – 8) =…
thanx elena :-)
To calculate the work done to move a charge from one position to another, we need to use the formula:
Work Done (W) = Charge (Q) × Change in Electric Potential (ΔV)
Given:
Charge (Q) = +180 nC (converting to Coulombs: 180 × 10^-9 C)
Change in Electric Potential (ΔV) = +8 V - (+24 V) = -16 V
Now, we have to convert the charge to Coulombs and the potential difference to volts:
Charge (Q) = 180 × 10^-9 C
Change in Electric Potential (ΔV) = -16 V
Plugging the values into the formula, we can calculate the work done:
W = Q × ΔV
W = (180 × 10^-9 C) × (-16 V)
W = -2.88 × 10^-6 J
Therefore, the work done to move the charge from a position with an electric potential difference of +24 V to another position with a potential difference of +8 V is approximately -2.88 × 10^-6 Joules.
To calculate the work required to move a charge in an electric field from one potential difference to another, you need to use the formula:
Work (W) = Charge (Q) * Change in Electric Potential (ΔV)
In this case, the charge (Q) is given as +180 nC (nanocoulombs), the change in electric potential (ΔV) is calculated by subtracting the final potential (+8V) from the initial potential (+24V).
ΔV = final potential - initial potential
ΔV = +8V - (+24V)
ΔV = +8V - 24V
ΔV = -16V
Now, plug the values into the formula:
W = Q * ΔV
W = +180 nC * (-16V)
When multiplying the charge by the change in electric potential, pay attention to the units. Convert the charge to coulombs since 1 nC is equal to 10^(-9) C:
W = (+180 nC * 10^(-9) C/nC) * (-16V)
W = +180 * 10^(-9) C * (-16V)
Now, multiply the numbers:
W = -2880 * 10^(-9) C⋅V
The work required to move the +180 nC charge from +24V to +8V is -2880 nC⋅V (or -2.880 μJ, microjoules). The negative sign indicates that work is done against the electric field.