Electric Potential
Electric Potential is electric potential energy (EPE) per unit of charge. (The unit of energy is the joule and the unit of charge is the coulomb.) Electric potential tells what the electric potential energy of a charged object will be for every coulomb of charge it has, or how many joules of energy there will be per coulomb.
Electric Potential Energy
Where the energy is conserved.
Electric Phenomena and Energy Analysis
- Electric phenomena can be analysed in terms of forces and energy.
- Kinetic energy increases when charges are moved around due to the acceleration from the forces.
- This configuration of charges also has a potential energy which decreases as kinetic energy increases.
- Total energy (symbol K) is conserved and equals the sum of kinetic energy and the potential energy (symbol U) in the system.
Energy Conservation and Potential Energy
- A change in kinetic energy corresponds to a change in the other direction for the potential energy.
- Knowing changes in kinetic energy can help calculate changes in potential energy.
- The change in kinetic energy is connected to the work done, which can be used to calculate changes in potential energy.
Positive and Negative Charges
- A configuration of positive charges has a positive overall potential energy.
- When charges move away from each other to an infinite distance (where their influence on each other is 0), the potential energy of the system is 0.
- Energy must be put into the system to bring the charges together against the forces, increasing its potential energy.
- A system of a positive and a negative charge has a negative potential energy.
- When these charges are brought together and start moving closer to each other, the potential energy decreases from 0 as the maximum.
Work and Potential Energy
- The change in potential energy is equal to minus the work involved in assembling the set of charges.
- Work is force times distance, but it also involves a direction, specifying the direction we’re moving through space and the connection between the direction we’re moving with the force that we’re fighting against, with the electric force.
Electric Potential and Units
- Electric potential is calculated by looking at the potential energy when a test charge (Q) is brought to a certain point (x, y, z), and dividing it by the test charge.
- The potential is a property of the source charge and exists in all of space around it.
- The potential due to a source charge is defined as the potential energy (U) if we put a test charge (Q) at the point (x, y, z).
- This potential represents the energetic influence of a source charge on all of space around it.
Electric Force and Work
- Electric force (E) is a vector, and work involves force times distance.
- Work is calculated as the dot product of force (F) and a small segment of the path (dR), i.e.,
F . dR. - The dot product considers the angle between the direction of the path and the force field.
- The total work is the integral of
F . dRover the entire path from the initial point to the final point, which is a line integral.
Path Independence and Potential Energy
- For electrostatics, the work done tells us about the change in potential energy, which depends only on space.
- The calculation of work is path-independent; only the starting and end points matter.
- The easiest path to calculate this is usually one that’s either parallel or perpendicular to the force.
- If the motion is parallel to the field, work is simply force times distance.
- If the motion is perpendicular to the force, no work is done (work equals 0).
Electric Potential
- The concept of electric potential describes the energy that a configuration of charges gives to any other charge that comes into the region.
- The potential is a property of the source charge and exists in all of space around it.
- The potential due to a source charge is defined as the potential energy (U) if we put a test charge (Q) at the point (x, y, z).
- This potential represents the energetic influence of a source charge on all of space around it.