Positive charge Q is distributed uniformly around a very thin conducting ring of radius a, as in Fig. 21.23. You measure the electric field E at points on the ring axis, at a distance x from the center of the ring, over a wide range of values of x. 

(a) Your results for the larger values of x are plotted in Fig. P21.94a as Ex² versus x. Explain why the quantity Ex² approaches a constant value as x increases. Use Fig. P21.94a to calculate the net charge Q on the ring.

(b) Your results for smaller values of x are plotted in Fig. P21.94b as E/x versus x. Explain why E/x approaches a constant value as x approaches zero. Use Fig. P21.94b to calculate a.

Figure P21.94

Fig.21.23

(a) (b) Ex (N - m/C) E/x (N/C - m) 50 700 45 40 600 35 500 30 400 25 x (m) 5 6 7 x (m) 20 0 1 2 3 4 300 0.1 0.2 0.3 dQ ds dE, dE