Question

A charge of 2.35 HC 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 N/C (b) 3.4 cm from the center of the ring N/C (c) 4.0 m from the center of the ring N/C (d) Find the field strength at 4.0 m using the approximation that the ring is a point charge at the origin. N/C (e) Compare your results for parts (c) and (d) by finding the ratio of the approximation to the exact result. (f) Is your approximation result a good one? Explain your answer. (Do this on paper. Your instructor may ask you to turn in your work.)

Answer 1

where,

$k=9\times 10^{9} N-m^{2}/C^{2}$

Integrating the above equation we get

$dE_{x}=\frac{kxQ}{(R^{2}+x^{2})^{3/2}}$

Question 1

GIVEN:

$Q=2.35\mu C$

$R=9.5cm$

$Distance from centre of ring,x=1.2cm$

$dE_{1.2}=\frac{9\times 10^{9}\times 1.2\times 2.35}{(9.5^{2}+1.2^{2})^{3/2}}$

$dE_{1.2}=2.89\times 10^{4}N/C$

QUESTION 2, x=3.4 cm

$dE_{3.4}=7\times 10^{4}N/C$

QUESTION 3,x=4m=400cm

$dE_{400}=132.0757N/C$

QUESTION 4, x=4m but ring is considered as point charge

Using Coulombs law, Electric strength due to point charge

$E_{x}=\frac{kQ}{x^{2}}$

$E_{400}=\frac{9\times 10^{9}\times 2.35\times 10^{-3}}{400^{2}}$

$E_{400}=132.1875N/C$

QUESTION 5, Ratio of approximation

$=\frac{132.1875}{132.0757}$

$=1.000846$

CONCLUSION

The electric field strength around the circular ring is almost seen to be identical to that of a point charge Q at the center of the ring