Why Does Work Done by Lightning Bolts Have Different Signs?

[Magna1]

Two questions.
1. a negative lightning bolt delivers a 15C charge from the ground to the BASE of a thunder cloud (Vpd = 5.0GV)
2. A positive lightning bolt delivers 20Ccharge from the Top of a thunder storm cloud to the ground (Vpd=30GV).

Both questions ask how much work is done to move the charge during the lightning strike. The question does give a distance but does that matter. using W=qVab I get my answer but BUT is one answer negative and one positive and why?
Thanks for the help in advance!

 

[ShawnD]

Originally posted by Magna1
Two questions.
1. a negative lightning bolt delivers a 15C charge from the ground to the BASE of a thunder cloud (Vpd = 5.0GV)
2. A positive lightning bolt delivers 20Ccharge from the Top of a thunder storm cloud to the ground (Vpd=30GV).

Both questions ask how much work is done to move the charge during the lightning strike. The question does give a distance but does that matter. using W=qVab I get my answer but BUT is one answer negative and one positive and why?

The distance does not matter as long as you know the voltage. The units work themselves out if you include them (which you should ALWAYS do). As for whether it will be positive or negative, they should both be positive since it just says "how much work is done to move the charge". Your answers can only be negative if the question gives a referance point.

I'll include the units in these so you'll see how they work out.
1).
E = Vq
E = (5x10^9 J/C)(15 C)
E = 7.5x10^10 J

2).
E = Vq
E = (30x10^9 J/C)(20 C)
E = 6x10^11 J

See how nicely the units work out? 1V = 1J/C

 

[M98Ranger]

The work done in both scenarios will be the same, as it is calculated by the formula W=qVab, where q is the charge and Vab is the potential difference. However, the sign of the work done may be different in each case.

In the first scenario, a negative lightning bolt delivers a 15C charge from the ground to the base of a thunder cloud with a potential difference of 5.0GV. This means that the charge is moving against the electric field, from a lower potential to a higher potential. Therefore, the work done will be negative, indicating that energy is being transferred from the lightning bolt to the electric field.

In the second scenario, a positive lightning bolt delivers a 20C charge from the top of a thunderstorm cloud to the ground with a potential difference of 30GV. In this case, the charge is moving with the electric field, from a higher potential to a lower potential. Therefore, the work done will be positive, indicating that energy is being transferred from the electric field to the lightning bolt.

The distance does not matter in this calculation as it is cancelled out when multiplied by the potential difference. The sign of the work done depends on the direction of the charge movement and the direction of the electric field. So, one answer will be negative and one will be positive based on the direction of the charge and electric field in each scenario.