A charge of 3.45 µC is uniformly distributed on a ring of radius 9.0 cm. Find th

Question

A charge of 3.45 µC is uniformly distributed on a ring of radius 9.0 cm. Find the electric field strength on the axis at the following locations.
(a) 1.2 cm from the center of the ring
answer in (N/C)

(b) 3.1 cm from the center of the ring
answer in (N/C)

(c) 4.0 m from the center of the ring
answer in (N/C)

(d) Find the field strength at 4.0 m using the approximation that the ring is a point charge at the origin.
answer in (N/C)

(e) Compare your results for parts (c) and (d) by finding the ratio of the approximation to the exact result.

Explanation / Answer

given charge on the ring q = 3.45* 10^-6C radius of ring R = 9.0cm = 0.09m    electric field strength   from the center of the ring is E = kqz/(z2+ R2)3/2    a) z = 1.2cm = 0.012m      then E = 9* 10^9 * 3.45 * 10^-6C * 0.012m/ * 0.0122 + 0.092)3/2                  = 47.4 * 10^4N/C b)z = 3.1cm = 0.031m                E = 9* 10^9 * 3.45 * 10^-6C * 0.031m/ * 0.0312 + 0.092)3/2                  = 111.6 * 10^4N/C c) z = 4.0m E = 9* 10^9 * 3.45 * 10^-6C * 4.0m/ * 4.02 + 0.092)3/2                  = 1.94*10^3N/C d) r = 4.0m    E = kq/r2      = 9 * 10^9 * 3.45 * 10^-6c/ 16      = 1.94 * 10^3N/C e) the ratio of part c and part d is                     Er/E = 1                  = 47.4 * 10^4N/C b)z = 3.1cm = 0.031m                E = 9* 10^9 * 3.45 * 10^-6C * 0.031m/ * 0.0312 + 0.092)3/2                  = 111.6 * 10^4N/C c) z = 4.0m E = 9* 10^9 * 3.45 * 10^-6C * 4.0m/ * 4.02 + 0.092)3/2                  = 1.94*10^3N/C d) r = 4.0m    E = kq/r2      = 9 * 10^9 * 3.45 * 10^-6c/ 16      = 1.94 * 10^3N/C e) the ratio of part c and part d is                     Er/E = 1                  = 111.6 * 10^4N/C c) z = 4.0m E = 9* 10^9 * 3.45 * 10^-6C * 4.0m/ * 4.02 + 0.092)3/2                  = 1.94*10^3N/C d) r = 4.0m    E = kq/r2      = 9 * 10^9 * 3.45 * 10^-6c/ 16      = 1.94 * 10^3N/C e) the ratio of part c and part d is                     Er/E = 1      = 9 * 10^9 * 3.45 * 10^-6c/ 16      = 1.94 * 10^3N/C e) the ratio of part c and part d is                     Er/E = 1

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