Difference between revisions of "Electric Potential"

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= Textbook =
= Textbook =
[https://openstax.org/books/university-physics-volume-2/pages/7-introduction University Physics Volume 2: Chapter 7]
[https://openstax.org/books/university-physics-volume-2/pages/7-introduction University Physics Volume 2: Chapter 7]


= Electric Potential Videos =
= Theory =
== Theory ==
 
=== Introduction ===
== Background: The Electric Force is a Conservative Force ==
The electric force is a conservative force, meaning that the work done by or against the electric force depends only on the initial and final positions, not on the path taken. This allows us to define the electric potential energy <math> U </math> in an electric field as the negative of the work <math> W </math> done by the electric force:
 
<math> U = -W </math>
 
where <math> W </math> is the work done by the electric force to move a charge within the field.
 
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== Electric Potential and Electric Potential Energy ==
=== Electric Potential Energy ===
=== Electric Potential Energy ===
'''Electric potential energy''' is the energy stored in a system of charges due to their positions in an electric field. This is similar to gravitational potential energy, where the position of an object in a gravitational field determines its potential energy.
=== Electric Potential (Voltage) ===
The '''electric potential''' <math> V </math> at a point is defined as the electric potential energy per charge:
<math> V = \frac{U}{q} </math>
Electric potential, also known as voltage, is measured in joules per coulomb (J/C).
=== Finding the Electric Potential Energy from the Electric Potential ===
If the electric potential <math> V </math> at a point is known, the electric potential energy <math> U </math> of a charge <math> q </math> placed at that point can be calculated as:
<math> U = q \cdot V </math>
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=== Electric Potential - Joules per Coulomb / Voltage ===
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=== Electric Potential due to a point charge ===
== Electric Potential due to a Point Charge at Rest ==
The electric potential <math> V </math> at a distance <math> r </math> from a point charge <math> Q </math> is given by:
<math> V = k_e \frac{Q}{r} </math>
where <math> k_e </math> is the electrostatic constant.
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== Potential Energy of a System of Charged Particles ==
The total electric potential energy of a system of charges is the sum of the potential energies between all pairs of charges in the system. For example, for three charges, <math> q_1, q_2, </math> and <math> q_3 </math>, the potential energy is:
<math> U = k_e \left( \frac{q_1 q_2}{r_{12}} + \frac{q_1 q_3}{r_{13}} + \frac{q_2 q_3}{r_{23}} \right) </math>
== Electric Potential and the Electric Field - Equipotential Lines ==
Equipotential lines represent points of equal electric potential in an electric field. They are always perpendicular to electric field lines. Moving along an equipotential line requires no work, as the electric potential remains constant.
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== Electric Potential, Current and Power ==
Electric potential difference, or voltage, causes current to flow in a conductor.
'''Current''' <math> I </math> is defined as the rate at which electric charge flows through a conductor:
<math> I = \frac{Q}{t} </math>
where <math> Q </math> is the charge in coulombs and <math> t </math> is time in seconds.
'''Power''' <math> P </math> is the rate of doing work, or work done per unit time. In an electric circuit, power represents the rate at which electrical energy is transferred or converted:
<math> P = \frac{W}{t} </math>
where <math> W </math> is the work done in joules and <math> t </math> is the time in seconds.


The power <math> P </math> delivered by an electric current <math> I </math> due to a potential difference <math> V </math> can be expressed as:


=== Electric Potential and the Electric Field ===
<math> P = V \cdot I </math>


=== Electric Potential, Current and Power ===
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== Example Problems ==
== Example Problems ==
=== Projectile Motion ===
Similar to projectile motion problems where gravity is the only force acting on an object, we can analyze the projectile motion of charged particles moving in an electric field, where they experience an electric force instead of gravitational force.
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= Electric Potential Simulations =
= Electric Potential Simulations =
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= Other Links =
= Other Links =
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Back to [[Electricity_and_Magnetism]]
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Next: [[Capacitors]]

Latest revision as of 15:32, 22 November 2024

Back to Electricity_and_Magnetism

Textbook

University Physics Volume 2: Chapter 7

Theory

Background: The Electric Force is a Conservative Force

The electric force is a conservative force, meaning that the work done by or against the electric force depends only on the initial and final positions, not on the path taken. This allows us to define the electric potential energy in an electric field as the negative of the work done by the electric force:

where is the work done by the electric force to move a charge within the field.



Electric Potential and Electric Potential Energy

Electric Potential Energy

Electric potential energy is the energy stored in a system of charges due to their positions in an electric field. This is similar to gravitational potential energy, where the position of an object in a gravitational field determines its potential energy.

Electric Potential (Voltage)

The electric potential at a point is defined as the electric potential energy per charge:

Electric potential, also known as voltage, is measured in joules per coulomb (J/C).


Finding the Electric Potential Energy from the Electric Potential

If the electric potential at a point is known, the electric potential energy of a charge placed at that point can be calculated as:


Electric Potential due to a Point Charge at Rest

The electric potential at a distance from a point charge is given by: where is the electrostatic constant.

Potential Energy of a System of Charged Particles

The total electric potential energy of a system of charges is the sum of the potential energies between all pairs of charges in the system. For example, for three charges, and , the potential energy is:

Electric Potential and the Electric Field - Equipotential Lines

Equipotential lines represent points of equal electric potential in an electric field. They are always perpendicular to electric field lines. Moving along an equipotential line requires no work, as the electric potential remains constant.

Electric Potential, Current and Power

Electric potential difference, or voltage, causes current to flow in a conductor.

Current is defined as the rate at which electric charge flows through a conductor: where is the charge in coulombs and is time in seconds.

Power is the rate of doing work, or work done per unit time. In an electric circuit, power represents the rate at which electrical energy is transferred or converted: where is the work done in joules and is the time in seconds.

The power delivered by an electric current due to a potential difference can be expressed as:



Example Problems

Projectile Motion

Similar to projectile motion problems where gravity is the only force acting on an object, we can analyze the projectile motion of charged particles moving in an electric field, where they experience an electric force instead of gravitational force.



Electric Potential Simulations


Other Links


Back to Electricity_and_Magnetism
Next: Capacitors