In Prob. 2.25, you found the potential on the axis of a uniformly charged disk:...

In Prob. 2.25, you found the potential on the axis of a uniformly charged disk:

(a) Use this, together with the fact that P_l (1) = 1, to evaluate the first three terms in the expansion (Eq. 3.72) for the potential of the disk at points off the axis, assuming r > R.

(b) Find the potential for r < R by the same method, using Eq. 3.66. [Note: You must break the interior region up into two hemispheres, above and below the disk. Do not assume the coefficients Al are the same in both hemispheres.]

Reference 3.72

Reference 3.66

Reference prob 25

Using Eqs. 2.27 and 2.30, find the potential at a distance z above the center of the charge distributions in Fig. 2.34. In each case, compute E = −∇V, and compare your answers with Ex. 2.1, Ex. 2.2, and Prob. 2.6, respectively. Suppose that we changed the right-hand charge in Fig. 2.34a to −q; what then is the potential at P? What field does that suggest? Compare your answer to Prob. 2.2, and explain carefully any discrepancy.

Eqs. 2.27

Eqs. 2.30

Reference example 2.1

Find the electric field a distance z above the midpoint between two equal charges (q), a distance d apart (Fig. 2.4a).

Reference example 2.1

Find the electric field a distance z above the midpoint of a straight line segment of length 2L that carries a uniform line charge λ (Fig. 2.6).

Reference prob.2.6

Find the electric field a distance z above the center of a flat circular disk of radius R (Fig. 2.10) that carries a uniform surface charge σ.What does your formula give in the limit R→∞? Also check the case z ≫R.

Reference figure 2.10

Reference prob.2.2

Find the electric field (magnitude and direction) a distance z above the midpoint between equal and opposite charges (±q), a distance d apart (same as Example 2.1, except that the charge at x = +d/2 is −q).

Reference example 2.1

Find the electric field a distance z above the midpoint between two equal charges (q), a distance d apart (Fig. 2.4a).