A charge of 2.30 µC is uniformly distributed on a ring of radius 9.5 cm. Find th

Question

A charge of 2.30 µC is uniformly distributed on a ring of radius 9.5 cm. Find the electric field strength on the axis at the following locations.

(a) 1.2 cm from the center of the ring
= the answer should be by N/C

(b) 3.6 cm from the center of the ring
= the answer should be by N/C

(c) 4.0 m from the center of the ring
= the answer should be by N/C

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

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

Explanation / Answer

Using an equation,   Ez = k Q z / (z2 + a2]3/2   

The electric field strength on the axis at the following locations.

(a) 1.2 cm from the center of the ring :

E1.2 = (9 x 109 Nm2/C2) (2.3 x 10-6 C) (0.012 m) / [(0.012 m)2 + (0.095 m)2]3/2

E1.2 = (9 x 109 Nm2/C2) (2.3 x 10-6 C) (0.012 m) / [(0.012 m) + (0.095 m)]3

E1.2 = 2.02 x 105 N/C

(b) 3.6 cm from the center of the ring :

E3.6 = (9 x 109 Nm2/C2) (2.3 x 10-6 C) (0.036 m) / [(0.036 m)2 + (0.095 m)2]3/2

E3.6 = (9 x 109 Nm2/C2) (2.3 x 10-6 C) (0.036 m) / [(0.036 m) + (0.095 m)]3

E3.6 = 3.31 x 105 N/C

(c) 4.0 m from the center of the ring :

E4 = (9 x 109 Nm2/C2) (2.3 x 10-6 C) (4 m) / [(4 m)2 + (0.095 m)2]3/2

E4 = (9 x 109 Nm2/C2) (2.3 x 10-6 C) (4 m) / [(4 m) + (0.095 m)]3

E4 = 1.2 x 103 N/C

(d) Using the approximation that the ring is a point charge at the origin.

The electric field strength is given as :

using an equation,   Ez = k Q / z2

E4 = (9 x 109 Nm2/C2) (2.3 x 10-6 C) / (4 m)2

E4 = 1.2 x 103 N/C

(e) The ratio of the approximation to the exact result which is given as :

1

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