A disk of radius 15.0 cm has a total charge 4.40 106 C distributed uniformly all

Question

A disk of radius 15.0 cm has a total charge 4.40 106 C distributed uniformly all over the disk.

(a) Using the exact equation, what is the electric field 1 mm from the center of the disk? (Enter the magnitude. Enter your answer to at least three significant figures.)

(b) Using the same exact equation, find the electric field 3 mm from the center of the disk. (Enter the magnitude. Enter your answer to at least three significant figures.)

(c) What is the percent difference between these two numbers?

Explanation / Answer

(a)

electric field 1 mm from the center of the disk is

E = [(Q/A) / 2*e0]*[1- z/R]

Q/A = 4.4*10^(-6) / pi*(0.15)^2 = 62.27*10^(-6)

E = [62.27*10^(-6) / 2*8.85*10^(-12)]*[1 - 0.001/0.15]

E = 3.49*10^6 N/C

(b)

E =  [62.27*10^(-6) / 2*8.85*10^(-12)]*[1 - 0.003/0.15]

E = 3.44*10^6 N/C

(c)

percent difference = (difference / average)*100

difference = (3.49 - 3.44)*10^6 = 0.05*10^6

average = 3.46*10^6

percent difference = (0.05*10^6 / 3.46*10^6)*100

percent difference = 1.44 %

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