electric potential

Examples of electric potential in the following topics:

• Electric Potential Due to a Point Charge

  • The electric potential of a point charge Q is given by $V=\frac{kQ}{r}$.
  • Recall that the electric potential is defined as the electric potential energy per unit charge
  • The electric potential tells you how much potential energy a single point charge at a given location will have.
  • The electric potential at a point is equal to the electric potential energy (measured in joules) of any charged particle at that location divided by the charge (measured in coulombs) of the particle.
  • The electric potential is a scalar while the electric field is a vector.

• Superposition of Electric Potential

  • We've seen that the electric potential is defined as the amount of potential energy per unit charge a test particle has at a given location in an electric field, i.e.
  • We've also seen that the electric potential due to a point charge is
  • Recall that the electric potential V is a scalar and has no direction, whereas the electric field E is a vector.
  • The summing of all voltage contributions to find the total potential field is called the superposition of electric potential.
  • Explain how the total electric potential due to a system of point charges is found

• Relation Between Electric Potential and Field

  • The electric potential at a point is the quotient of the potential energy of any charged particle at that location divided by the charge of that particle.
  • Thus, the electric potential is a measure of energy per unit charge.
  • In terms of units, electric potential and charge are closely related.
  • In a more pure sense, without assuming field uniformity, electric field is the gradient of the electric potential in the direction of x:
  • Explain the relationship between the electric potential and the electric field

• Energy Conservation

  • This phenomenon can be expressed as the equality of summed kinetic (Ekin) and electric potential (Eel) energies:
  • In all cases, a charge will naturally move from an area of higher potential energy to an area of lower potential energy.
  • At the instant at which the field is applied, the motionless test charge has 0 kinetic energy, and its electric potential energy is at a maximum.
  • where m and v are the mass and velocity of the electron, respectively, and U is the electric potential energy.
  • Formulate energy conservation principle for a charged particle in an electric field

• Potentials and Charged Conductors

  • All points within a charged conductor experience an electric field of 0.
  • However, having the electric field equal to zero at all points within a conductor, the electric potential within a conductor is not necessarily  equal to zero for all points within that same conductor.
  • This can be proven by relating electric field and potential.
  • Rewriting U as the product of charge (q) and potential difference (V), and force as the product of charge and electric field (E), we can assert:
  • Thus we can conclude that, given that the electric field is constantly 0 for any location within the charged conductor, the potential difference in that same volume needs to be constant and equal to 0.

• Potential Energy Curves and Equipotentials

  • A potential energy curve plots potential energy as a function of position; equipotential lines trace lines of equal potential energy.
  • In and , if you travel along an equipotential line, the electric potential will be constant.
  • So, every point that is the same distance from the point charge will have the same electric potential energy.
  • Recall that work is zero if force is perpendicular to motion; in the figures shown above, the forces resulting from the electric field are in the same direction as the electric field itself.
  • So we note that each of the equipotential lines must be perpendicular to the electric field at every point.

• Electric Field and Changing Electric Potential

  • Any charge will create a vector field around itself (known as an electric field).
  • As the test charge moves, the potential between it and another charge changes, as does the electric field.
  • The relationship between potential and field (E) is a differential: electric field is the gradient of potential (V) in the x direction.
  • Thus, as the test charge is moved in the x direction, the rate of the its change in potential is the value of the electric field.
  • Calculate the electric potential created by a charge distribution of constant value

• Conductors and Insulators

  • An insulator is a material in which, when exposed to an electric field, the electric charges do not flow freely—it has a high resistivity.
  • All conductors contain electric charges that, when exposed to a potential difference, move towards one pole or the other.
  • The positive charges in a conductor will migrate towards the negative end of the potential difference; the negative charges in the material will move towards the positive end of the potential difference.
  • This flow of charge is electric current.
  • Insulators are materials in which the internal charge cannot flow freely, and thus cannot conduct electric current to an appreciable degree when exposed to an electric field.

• Uniform Electric Field

  • An electric field that is uniform is one that reaches the unattainable consistency of being constant throughout.
  • A uniform field is that in which the electric field is constant throughout.
  • Equations involving non-uniform electric fields require use of differential calculus.
  • Uniformity in an electric field can be approximated by placing two conducting plates parallel to one another and creating a potential difference between them.
  • For the case of a positive charge q to be moved from a point A with a certain potential (V1) to a point B with another potential (V2), that equation is:

• Dipole Moments

  • The electric dipole moment is a measure of polarity in a system.
  • Among the subset of electric dipole moments are transition dipole moments, molecular dipole moments , bond dipole moments, and electron electric dipole moments.
  • It is brought on by the need to minimize potential energy.
  • Torque (τ) can be calculated as the cross product of the electric dipole moment and the electric field (E), assuming that E is spatially uniform:
  • Relate the electric dipole moment to the polarity in a system