A 4.25 mu_C charge is uniformly distributed on a ring of radius 9 cm. Find the e

Question

A 4.25 mu_C charge is uniformly distributed on a ring of radius 9 cm. Find the electric field on the axis at 0.9 cm from the center of the ring. The value of the Coulomb constant is 8.99 Times 10^9 N middot m^2/C^2. Answer in units of N/C. Find the electric field on the axis at 4.2 cm from the center of the ring. Answer in units of N/C. Find the electric field on the axis at 4 m from the center of the ring. Answer in units of N/C. Find the electric field on the axis at 4 m assuming that the ring is a point charge at the origin. Answer in units of N/C.

Explanation / Answer

We know that the magnitude of electric field at a distance z on the axis of the ring carruing charge Q and having radius R is given by:

Ez = k Q z/ (z^2 + a^2)^3/2

12) z = 0.9 cm = 0.009 m

Ez = (8.99 x 10^9) (4.25 x 10^-6) x 0.009 / (0.009^2 + 0.09^2)^(3/2) = 4.65 x 10^5 N/C

Hence, Ez = 4.65 x 10^5 N/C

13)z = 4.2 cm = 0.042 m

Ez = (8.99 x 10^9) (4.25 x 10^-6) x 0.042 / (0.042^2 + 0.09^2)^(3/2) = 0.254 N/C

Ez = 1.64 x 10^6 N/C

14)z = 4 m

Ez = (8.99 x 10^9) (4.25 x 10^-6) x 4 / ( 4^2 + 0.09^2)^(3/2)

Ez = 2.39 x 10^3 N/C

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