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Electric field due to charge distributions cont’d

Electric field due to charge distributions cont’d. Class Object. Reinforce the ideas and problem solving strategies used for the example of a rod with a uniform charge distribution.

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Electric field due to charge distributions cont’d

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  1. Electric field due to charge distributions cont’d

  2. Class Object • Reinforce the ideas and problem solving strategies used for the example of a rod with a uniform charge distribution.

  3. Be able to identify the similarities between the strategy for calculating the electric field due to a rod and a ring. • Be able to apply the strategies learnt to non-uniform charge distributions and to other shapes and configurations.

  4. Electric Field due to a ring of uniform charge

  5. Electric Field due to a ring of uniform charge • Consider a ring of radius R, with uniform charge Q. What is the total electric field ata point P a distance z along an axis through its centre?

  6. Electric Field due to a ring of uniform charge • Consider a ring of radius R, with uniform charge Q. What is the total electric field ata point P a distance z along an axis through its centre? ds

  7. Electric Field due to a ring of uniform charge • Applying the concepts from the previous example, we consider the charge per unit length.

  8. Electric Field due to a ring of uniform charge • Applying the concepts from the previous example, we consider the charge per unit length. • In this case, .

  9. Electric Field due to a ring of uniform charge • Applying the concepts from the previous example, we consider the charge per unit length. • In this case, . • The electric field due to a charge element ds is

  10. Electric Field due to a ring of uniform charge • Because of symmetry we that again the horizontal components cancel. Therefore we write that,

  11. Electric Field due to a ring of uniform charge • Because of symmetry we that again the horizontal components cancel. Therefore we write that, • Where r and θ are constant.

  12. Electric Field due to a ring of uniform charge • Therefore the integral becomes,

  13. Electric Field due to a ring of uniform charge • Therefore the integral becomes, • This integral is simply over the circumference so that,

  14. Electric Field due to a ring of uniform charge • From the diagram we can substitute for the cosine.

  15. Electric Field due to a ring of uniform charge • From the diagram we can substitute for the cosine.

  16. Electric Field due to a ring of uniform charge • After some algebra we write that,

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