Consider a ring of charge with total charge Q and with a radiusof R, centered at the origin in the x-y plane. Determine theelectric field at any location along the z-axis. Fill in theBLANKS.
1. Because of symmetry, the electric field at any point on thez-axis will always be in the _________________
2. Therefore, we only need to consider the ______________________of any contribution to the electric field from a single element ofcharge on the ring.
3. To calculate the electric field at a point on the z-axis, we aregoing to integrate around the ring of charge. The radius of thering is constant and therefore it makes sense for the variable ofintegration to be ___________________.
4. The z-component of the electric field from a single element ofcharge (dQ) is _______________________________________ (write in terms of dQ, zand r-the distance from the element of charge to the pointp).
5. To calculate the charge on dQ we need to know the charge perunit length which is given by__________________________________________
6. An element of charge, dQ, has a length of _____________ (answerin terms of R and Î) and a charge of______________________________.
7. The distance from this element to the point p is given by:______________________
8. Rewriting # 4 in terms of #6 and #7 we get that_______________________________
9. Now to find the total electric field for a point along thez-axis we simply integrate around the ring making_____________________________________________
10. Suppose that z was really really large (much larger than R).What would you expect the electric field to behave as?
11. Suppose that z was zero. What do you expect the electric fieldto be?
12. Does your solution match these limiting situations?Explain.
