For a disk of radius R-46 cm and Q = 3 x 10-0 C, calculate the electric field 2

Question

For a disk of radius R-46 cm and Q = 3 x 10-0 C, calculate the electric field 2 mm from the center of the disk using all three equations. (Enter the magnitude.) (QIA) 2 QIA 2e , and E first N/C Esccond N/C Ethird N/C How good are the approximate equations at this distance? Both the second and third values are more than 10% different from the first, most accurate value. O The second value is within 5% of the first, most accurate value. The third value, however, is more than 10% different from the first value O Both the second and third values are within 5% of the first, most accurate value. O The third value is within 5% of the first, most accurate value. The second value, however, is more than 10% different from the first value For the same disk, calculate E at a distance of 8 cm (80 mm) using all three equations first = N/C N/C third N/C How good are the approximate equations at this distance? Both the second and third values are more than 10% different from the first, most accurate value The second value is within 5% of the first, most accurate value. The third value, however, is more than 10% different from the first value Both the second and third values are within 5% of the first, most accurate value. O The third value is within 5% of the first, most accurate value. The second value, however, is more than 10% different from the first value

Explanation / Answer

When, R=0.46m,

z=0.002m, Q=3*10^-3 C= 0.003 C

A=R2 = 3.14*0.46^2 = 0.66m2

Efirst = [(Q/A)/(20)]*[1-z/sqrt(R2+z2)] = [(0.003/0.66)/(2*8.85*10^-12)]*[1-0.002/sqrt(0.462+0.0022)] = 2.5569*10^8 N/C

Esecond = [(Q/A)/(20)]*[1-z/R] = [(0.003/0.66)/(2*8.85*10^-12)]*[1-0.002/0.46] = 2.5569*10^8 N/C

Ethird = (Q/A)/(20) = [(0.003/0.66)/(2*8.85*10^-12)] = 2.5680*10^8 N/C

The second value is within 10% of the first value, most accurate value. The third value , however, is more than 10% different from the first value

When, R=0.08m,

z=0.002m, Q=3*10^-3 C= 0.003 C

A=R2 = 3.14*0.08^2 = 0.02m2

Efirst = [(Q/A)/(20)]*[1-z/sqrt(R2+z2)] = [(0.003/0.02)/(2*8.85*10^-12)]*[1-0.002/sqrt(0.082+0.0022)] = 8.4162*10^9 N/C

Esecond = [(Q/A)/(20)]*[1-z/R] = [(0.003/0.02)/(2*8.85*10^-12)]*[1-0.002/0.08] = 8.2627*10^9 N/C

Ethird = (Q/A)/(20) = [(0.003/0.02)/(2*8.85*10^-12)] = 8.4746*10^9 N/C

The third value is within 10% of the first value, most accurate value. The second value , however, is more than 10% different from the first value

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