Question
Part A
If you can find symmetries in a physical situation, you can often greatly simplify your calculations. In this part you will find a symmetry in the annular ring before calculating the potential along the z axis through the ring's center in Part B.
Consider three sets of points: points lying on the vertical line A; those on circle B; and those on the horizontal line C, as shown in the figure. Which set of points makes the same contribution toward the potential calculated at any point along the axis of the annulus? (Figure 2)
1-points on line A
2-points on circle B
3- points on line C
An annular ring with a uniform surface charge density sits in the xy plane, with its center at the origin of the coordinate axes. The annulus has an inner radius r1 and outer radius r2 If you can find symmetries in a physical situation, you can often greatly simplify your calculations. In this part you will find a symmetry in the annular ring before calculating the potential along the z axis through the ring's center in Part B. Consider three sets of points: points lying on the vertical line A; those on circle B; and those on the horizontal line C, as shown in the figure. Which set of points makes the same contribution toward the potential calculated at any point along the axis of the annulus? (Figure 2) points on line A points on circle B points on line C By exploiting the above symmetry, or otherwise, calculate the electric potential V at a point on the axis of the annulus a distance d from its center. Be sure to visualize this carefully; the point we are interested in lies along the axis of the annulus, but is above the plane of the annulus by a distance d . Express your answer in terms of some or all of the variables , r1 , r2 , and d . Use k(=14 ϵ0) V=
Explanation / Answer
part A is point B