anonymous
  • anonymous
electric flux is defined as the total number of lines of force through a unit normal area..but I find it a little raw explanation...isn't it possible to draw infinite lines around a charge??!!
MIT 8.02 Electricity and Magnetism, Spring 2002
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schrodinger
  • schrodinger
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anonymous
  • anonymous
hehehe that is tricky (it's me again) The 100% correct definition for electric flux would be this: \[\Phi(\vec E) = \vec A \cdot \vec E\] you'll note that both A, which represents the Area, and E are vectors. This because this is a dot product between vectors, which can be expanded as: \[\Phi (\vec E) = |\vec A|\cdot |\vec E| \cdot \cos\theta\] Where theta is the angle between the direction of the field and the normal to the surface. (we always define the 'direction' of an Area with the line perpendicular to it.) Drawing: |dw:1378772188535:dw| Notice that the cosine of an angle it's maximum when the angle is 0, in fact when theta is 0 the E field is perfectly perpendicular to the surface, thus resulting in maximum flux! So, what about these lines your notes talk about? That is kinda misleading, it is more of a qualitative stating, rather than quantitative, but it works like this: If you keep the density of the E field lines consistent and proportional to the intensity of the field, for example: this is WRONG: |dw:1378772578364:dw| this is RIGHT! |dw:1378772682322:dw| you can understand that if you put an Area where more lines are passing through (close to the charge) you'll also have a greater flux. (E field is bigger.) But the correct way of thinking about the flux is of a product between the area and the intensity of the field. Want to be 100% correct? (this is needed for funky surfaces) Flux as the SUM of the products of infinitesimal Area pieces and the field intensity in those 'points'. \[\Phi(\vec E) = \int\limits_{Area} \vec E \cdot d\vec A\]
anonymous
  • anonymous
Want to hit your question very hard: NO! you can't draw as many lines as you want! Again (hehehehe) you have to put up a convention. Much like when you plot a graph and you say that 1 square of your squared paper corresponds to 1 cm, when you draw lines to represent a field, there should be a relation between the intensity of the field and the lines themselves (even tho we never try to figure it out for real) The important thing is: when you zoom in, the number of lines stays the same! Hope it helped.
anonymous
  • anonymous
you nailed it man..thanks

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anonymous
  • anonymous
mr mathavraj you are about correct but keep i mnd that feild lines depends on the strength of the charged partical you got it.
anonymous
  • anonymous
Yes, as Gywhard explained, we only need to draw representative sample of the field lines, and should be consistent: if you assign a charge 1 C with 10 lines, then 2 C will have 20 lines, 0.5 C will have 5 lines, and so on. In two dimensions, it is rather elusive, but in three dimensions, \[\frac{ 1 }{ r^{2} }\] can be shown compatible with Coulomb's law of electricity

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