For a disk of radius 14 cm with uniformly distributed charge 2 × 10−6 c, calculate the magnitude of the electric field on the axis of the disk, 7 mm from the center of the disk, using each of the following equations
a) e = (q/a) / 2ε0 [1- z / (r2+z2)1/2]
n/c
b) e ≈ q/a / 2ε0 [1 − z/r]
n/c
c) e ≈ q/a / 2ε0
n/c
d) how good are the approximate equations at this distance?
a) both the second and third values are more than 3% different from the first, most accurate value.
b) the second value is within 1% of the first, most accurate value. the third value, however, is more than 3% different from the first value.
c) both the second and third values are within 1% of the first, most accurate value. the third value is within 1% of the first, most accurate value.
d) the second value, however, is more than 3% different from the first value.
e) at what distance does the least accurate approximation for the electric field give a result that is closest to the most accurate:
a) at a distance r/2
b) close to the disk
c) at a distance r
d) far from the disk