If you do 10 J of work to push a charge into an electric field and then release the charge, as it flies past its starting position, its kinetic energy is less than 10 J. 10 J. more than 10 J.
The correct answer and explanation is:
Correct Answer: 10 J
Explanation:
When you do 10 joules (J) of work to move a charge into an electric field, you are increasing its electric potential energy by 10 J. This energy is stored in the charge-field system.
According to the work-energy principle and conservation of energy, energy cannot be created or destroyed, only transformed from one form to another. In this case:
- You input 10 J of mechanical work.
- That work is stored as electric potential energy in the system.
- When the charge is released, this potential energy is converted into kinetic energy as the electric field accelerates the charge.
Assuming no energy losses (i.e., no friction, no radiation, or other dissipative forces), all 10 J of potential energy becomes 10 J of kinetic energy by the time the charge returns to its original position.
Why Not More or Less Than 10 J?
- Less than 10 J: This would imply some energy was lost to friction or other forces. But the problem does not mention any such losses, so we assume an ideal system.
- More than 10 J: That would violate conservation of energy because you’d be getting more kinetic energy out than the energy you put in—essentially, creating energy from nowhere.
So, as the charge flies past its starting position, it has converted its 10 J of stored potential energy into 10 J of kinetic energy.
This scenario is analogous to lifting a mass in a gravitational field. If you lift a ball and do 10 J of work, and then drop it, it will have 10 J of kinetic energy when it returns to its original height—no more, no less.