E field calculations for continuous charge distributions

In summary, when calculating electric field using continuous charge distribution, there are three useful tools: utilizing symmetry, expressing charge in terms of charge density, and checking the answer at large r to confirm its correctness. Checking the answer at large r involves comparing it to Coulomb's law for a point charge, which can help identify any errors in the calculation.
  • #1
kiwibird4
8
0
so I was reviewing my textbook on calculating electric field when we can assume a continuous charge distribution and they said three useful tools are
(1) making use of symmetry
(2) expressing the charge dq in terms of charge density lambda
(3) and checking the answer at the limit of large r which serves as an indication of the correctness of the answer -- if result does not check at large r, your result has to be wrong (giancoli textbook).

Anyway, I understand the usefulness of 1 and 2 but do not fully understand what number 3 is talking about or how to check the answer in that way? Can anyone explain further what they are referring to or maybe give an example
 
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  • #2
For example, if you're calculating the electric field around a ring or disc or sphere or something, then you should expect that for ##r## that are very far away, since the object will look essentially like a point, the electric field equation should look like coulomb's law for a point charge.
 

Related to E field calculations for continuous charge distributions

1. How do you calculate the electric field for a continuous charge distribution?

To calculate the electric field for a continuous charge distribution, you can use the formula E = k∫(dq/r²)cosθ, where k is the Coulomb's constant, dq is a small element of charge, r is the distance between the charge element and the point where the field is being measured, and θ is the angle between the direction of the field and the line connecting the charge element and the point.

2. What is a continuous charge distribution?

A continuous charge distribution is a distribution of charge over a continuous region of space, rather than at discrete points. This could be in the form of a line, surface, or volume of charge.

3. How does the electric field vary for a continuous charge distribution?

The electric field varies for a continuous charge distribution because the charge is spread out over a larger region, rather than concentrated at a single point. This results in a more gradual decrease in the electric field as you move away from the charge distribution.

4. Can the electric field be negative for a continuous charge distribution?

Yes, the electric field can be negative for a continuous charge distribution. This occurs when the direction of the field is opposite to the direction of the positive charge. In other words, the field points towards the negative charges in the distribution.

5. How do you handle non-uniform charge distributions when calculating the electric field?

When dealing with non-uniform charge distributions, you can break the distribution into small charge elements and use the principle of superposition to calculate the total electric field. This involves adding up the contributions from each individual charge element using the formula E = k∫(dq/r²)cosθ. Alternatively, you can use integration to find the total electric field for a continuous charge distribution.

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