Question

A charge of 2.35 HC is uniformly distributed on a ring of radius 9.5 cm. Find the elecric field strength on the axis at the following locations. (a) 1.2 cm from the center of the ring 2.8900 (b) 3.4 cm from the center of the ring 7e4 N/C (c) 4.0 m from the center of the ring 132.0757 x N/C (d) Find the field strength at 4.0 m using the approximation that the ring is a point charge at the origin. 132.1875x N/C (e) Compare your results for parts (c) and (d) by finding the ratio of the approximation to the exact result. 1.000846

Answer 1

Solution)Given

Charge on the ring q = 2.35* 10^-6C

radius of ring R = 9.5 cm = 0.095 m

We know, Electric field strength from the center of the ring is given by-

E = kqz/(z^2+ R^2)3/2

a) z = 1.2cm = 0.012m

So, E = 9* 10^9 * 2.35 * 10^-6C * 0.012m/ (0.012* 0.012 + 0.095^2)^3/2

= 28.9 * 10^4N/C (Ans)

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b)z = 3.4cm = 0.034 m

E = 9* 10^9 * 2.35 * 10^-6C * 0.034m/ (0.034* 0.034 + 0.095^2)^3/2

= 70.0* 10^4N/C

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c) z = 4.0m

E = 9* 10^9 * 2.35 * 10^-6C * 4.0m/(4 * 4+ 0.095^2)^3/2

= 1320.75N/C

d) r = 4.0m

E = kq/r^2

= 9 * 10^9 * 2.35 * 10^-6c/ 16

= 1321.875 N/C

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Good luck!:)