184_notes:examples:week5_flux_dipole

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184_notes:examples:week5_flux_dipole [2017/09/25 14:08] – [Solution] tallpaul184_notes:examples:week5_flux_dipole [2018/07/24 15:02] (current) – curdemma
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 +[[184_notes:eflux_curved|Return to Electric Flux through Curved Surfaces notes]]
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 =====Example: Flux from a Dipole===== =====Example: Flux from a Dipole=====
 Suppose you have a two charges, one with value $5 \mu\text{C}$, the other with value $-5 \mu\text{C}$. There are at separate locations, a distance $1 \text{ m}$ apart, and they can be modeled as a dipole. What is the flux through a cylinder with radius $4 \text{ m}$ and length $16 \text{ m}$ that encloses this dipole? Suppose you have a two charges, one with value $5 \mu\text{C}$, the other with value $-5 \mu\text{C}$. There are at separate locations, a distance $1 \text{ m}$ apart, and they can be modeled as a dipole. What is the flux through a cylinder with radius $4 \text{ m}$ and length $16 \text{ m}$ that encloses this dipole?
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 ===Representations=== ===Representations===
   * We represent the situation with the following diagram.   * We represent the situation with the following diagram.
-{{ 184_notes:5_dipole_cylinder.png?300 |Dipole and Gaussian cylinder}}+[{{ 184_notes:5_dipole_cylinder.png?300 |Dipole and Gaussian cylinder}}]
 ====Solution==== ====Solution====
 First, notice that we probably do not want to do any calculations here, since the it will not be fun to take a dot-product of the dipole's electric field and the area-vector, and it will get very messy very quickly when we start integrating over the surface of the cylinder. Instead, we evaluate the situation more qualitatively. Consider the electric field vectors of the dipole near the surface of the cylinder: First, notice that we probably do not want to do any calculations here, since the it will not be fun to take a dot-product of the dipole's electric field and the area-vector, and it will get very messy very quickly when we start integrating over the surface of the cylinder. Instead, we evaluate the situation more qualitatively. Consider the electric field vectors of the dipole near the surface of the cylinder:
-{{ 184_notes:5_dipole_field_lines.png?300 |Dipole Electric Field Lines}}+[{{ 184_notes:5_dipole_field_lines.png?300 |Dipole Electric Field Lines}}]
  
 Notice that the vectors near the positive charge are leaving the cylinder, and the vectors near the negative charge are entering. Not only this, but they are mirror images of each other. Wherever an electric field vector points out of the cylinder on the right side, there is another electric field vector on the left that is pointing into the cylinder at the same angle. These mirror image vectors also have the same magnitude, though it is a little tougher to visualize. Notice that the vectors near the positive charge are leaving the cylinder, and the vectors near the negative charge are entering. Not only this, but they are mirror images of each other. Wherever an electric field vector points out of the cylinder on the right side, there is another electric field vector on the left that is pointing into the cylinder at the same angle. These mirror image vectors also have the same magnitude, though it is a little tougher to visualize.
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  • Last modified: 2017/09/25 14:08
  • by tallpaul