Potential Due To Different Charge Distributions

Definition of Electron Volt (eV)

- In the previous lectures, we discussed the concept of potential difference and electric potential. - The potential difference between two points in an electric field is defined as the amount of work done per unit charge in moving a test charge from one point to another. - In this lecture, we will extend our understanding of potential to different charge distributions. - We will also introduce the concept of the electron volt (eV) as a unit of energy. - The electric potential at a point due to a point charge is given by Coulomb's law. - For a point charge Q Q at a distance r r from the point, the electric potential V V is given by the equation: V=kQr V = \frac{kQ}{r} Where k k is the electrostatic constant. - The potential due to a point charge decreases as the distance from the charge increases. - Now, let's consider the potential due to a collection of point charges. - The total potential at a point due to multiple charges is the algebraic sum of the potentials due to each individual charge. - If there are n n charges Qi Q_i at distances ri r_i from the point, the total potential V V at that point is given by: V=kQ1r1+kQ2r2+kQ3r3+…+kQnrn V = \frac{kQ_1}{r_1} + \frac{kQ_2}{r_2} + \frac{kQ_3}{r_3} + \ldots + \frac{kQ_n}{r_n} - The principle of superposition holds true for electric potential. - When dealing with continuous charge distributions, we need to use integrals to find the potential at a point. - For a linear charge density λ(x) \lambda(x) , the potential dV dV at a point P P due to a small segment dx dx is given by: dV=kλ(x)rdx dV = \frac{k\lambda(x)}{r}dx - To find the potential due to the entire distribution, we integrate the above equation over the entire length of the distribution. - - For a surface charge density σ(x,y) \sigma(x, y) , the potential dV dV at a point P P due to an element dA dA is given by: dV=kσ(x,y)rdA dV = \frac{k\sigma(x, y)}{r}dA - To find the potential due to the entire surface, we integrate the above equation over the entire surface area.

  • For a volume charge density ρ(x,y,z) \rho(x, y, z) , the potential dV dV at a point P P due to a small volume element dτ d\tau is given by: dV=kρ(x,y,z)rdτ dV = \frac{k\rho(x, y, z)}{r}d\tau

  • To find the potential due to the entire volume, we integrate the above equation over the entire volume.

  • We can also define the electric potential using the electric field ( E E ) at a point.

  • The electric field at a point due to a charge distribution is defined as the force experienced by a unit positive test charge placed at that point.

  • The potential at a point is the work done in bringing a unit positive test charge from infinity to that point against the electric field.

  • We can use the electric field equation to find the potential due to a charge distribution.

  • Now, let’s introduce the concept of the electron volt (eV).

  • The electron volt is a unit of energy commonly used in atomic and nuclear physics.

  • It is defined as the amount of energy gained or lost by an electron when it is accelerated through an electric potential difference of one volt.

  • 1 eV is equivalent to the charge of an electron ( 1.6×10−19 1.6 \times 10^{-19} C) multiplied by one volt.

  • The electron volt is a convenient unit for measuring energies on an atomic scale.

  • Energy is quantized in atomic and subatomic systems, and the electron volt allows us to easily express these energy levels.

  • For example, the ionization energy of hydrogen is 13.6 eV.

  • It represents the minimum amount of energy required to ionize hydrogen atom, i.e., to remove an electron from the atom.

  • In summary, in this lecture, we discussed the potential due to different charge distributions.

  • We explained the concept of the electron volt as a unit of energy.

  • We also learned how to calculate the potential due to point charges, linear charge distributions, surface charge distributions, and volume charge distributions.

  • Next, we will solve numerical problems to reinforce our understanding of these concepts.

  • Stay tuned for the next lecture!

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Potential Due To Different Charge Distributions Definition of Electron Volt (eV) - In the previous lectures, we discussed the concept of potential difference and electric potential. - The potential difference between two points in an electric field is defined as the amount of work done per unit charge in moving a test charge from one point to another. - In this lecture, we will extend our understanding of potential to different charge distributions. - We will also introduce the concept of the electron volt (eV) as a unit of energy. - The electric potential at a point due to a point charge is given by Coulomb's law. - For a point charge $ Q $ at a distance $ r $ from the point, the electric potential $ V $ is given by the equation: $ V = \frac{kQ}{r} $ Where $ k $ is the electrostatic constant. - The potential due to a point charge decreases as the distance from the charge increases. - Now, let's consider the potential due to a collection of point charges. - The total potential at a point due to multiple charges is the algebraic sum of the potentials due to each individual charge. - If there are $ n $ charges $ Q_i $ at distances $ r_i $ from the point, the total potential $ V $ at that point is given by: $ V = \frac{kQ_1}{r_1} + \frac{kQ_2}{r_2} + \frac{kQ_3}{r_3} + \ldots + \frac{kQ_n}{r_n} $ - The principle of superposition holds true for electric potential. - When dealing with continuous charge distributions, we need to use integrals to find the potential at a point. - For a linear charge density $ \lambda(x) $ , the potential $ dV $ at a point $ P $ due to a small segment $ dx $ is given by: $ dV = \frac{k\lambda(x)}{r}dx $ - To find the potential due to the entire distribution, we integrate the above equation over the entire length of the distribution. - - For a surface charge density $ \sigma(x, y) $ , the potential $ dV $ at a point $ P $ due to an element $ dA $ is given by: $ dV = \frac{k\sigma(x, y)}{r}dA $ - To find the potential due to the entire surface, we integrate the above equation over the entire surface area. For a volume charge density $ \rho(x, y, z) $ , the potential $ dV $ at a point $ P $ due to a small volume element $ d\tau $ is given by: $ dV = \frac{k\rho(x, y, z)}{r}d\tau $ To find the potential due to the entire volume, we integrate the above equation over the entire volume. We can also define the electric potential using the electric field ( $ E $ ) at a point. The electric field at a point due to a charge distribution is defined as the force experienced by a unit positive test charge placed at that point. The potential at a point is the work done in bringing a unit positive test charge from infinity to that point against the electric field. We can use the electric field equation to find the potential due to a charge distribution. Now, let’s introduce the concept of the electron volt (eV). The electron volt is a unit of energy commonly used in atomic and nuclear physics. It is defined as the amount of energy gained or lost by an electron when it is accelerated through an electric potential difference of one volt. 1 eV is equivalent to the charge of an electron ( $ 1.6 \times 10^{-19} $ C) multiplied by one volt. The electron volt is a convenient unit for measuring energies on an atomic scale. Energy is quantized in atomic and subatomic systems, and the electron volt allows us to easily express these energy levels. For example, the ionization energy of hydrogen is 13.6 eV. It represents the minimum amount of energy required to ionize hydrogen atom, i.e., to remove an electron from the atom. In summary, in this lecture, we discussed the potential due to different charge distributions. We explained the concept of the electron volt as a unit of energy. We also learned how to calculate the potential due to point charges, linear charge distributions, surface charge distributions, and volume charge distributions. Next, we will solve numerical problems to reinforce our understanding of these concepts. Stay tuned for the next lecture!