Uniformly charged rod concept question

[StephenDoty]

If a uniformly charged rod is bisected in the middle the limits of integration would be (-L/2) to (L/2)? Thus the formula would be the integral from (-L/2) to (L/2) of k*dq/r^2. Now of course there might be an angle so cos(theta) and sin(theta) would need to be added.

If the point at which we are trying to find the electric field at is either to the left or right of the bisecting line, would the limits of integration be one end number to the other end number? like if a rod extended from (0,0) to (6,0), the limits of integration would be 0 to 6 for a point to the left or right of the bisecting line? Thus the formula would be the integral from the left or bottom to the right or top of k*dq/r^2. Of course the components would need to be foun using cos and sin.

But do I have the concept of the limits of integration correct?
Thanks.
Stephen

 

[jbsteele]

Yes, you have the concept of the limits of integration correct. The limits of integration for a point to the left or right of the bisecting line would indeed be from one end number to the other end number. As you mentioned, cos and sin functions would need to be added to account for any angle that may exist.

 

[baba89]

Yes, you have the concept of limits of integration correct. When dealing with a uniformly charged rod, the limits of integration represent the length of the rod, which is from (-L/2) to (L/2) when bisected in the middle. This means that the electric field at any point along the rod can be calculated by integrating from the left or bottom end to the right or top end, depending on the position of the point in question. The use of cos and sin is necessary to take into account any angle that may exist between the point and the rod. Overall, your understanding of the concept and formula for calculating the electric field is correct.