Please show all work. Thanks The total electric field at a point on the axis of

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Please show all work. Thanks

The total electric field at a point on the axis of a uniformly charged disk, which has a radius R and a uniform charge density of , is given by the following expression, where x is the distance of the point from the disk.

Consider a disk of radius R = 3.06 cm having a uniformly distributed charge of +5.68 µC.
(a) Using the expression above, compute the electric field at a point on the axis and 3.18 mm from the center.
_________N/C

(b) Explain how the answer to part (a) compares with the field computed from the near-field approximation E = /20.

(c) Using the first expression above, compute the electric field at a point on the axis and 31.8 cm from the center of the disk.
__________ N/C

(d) Explain how the answer to part (c) compares with the electric field obtained by treating the disk as a +5.68-µC charged particle at a distance of 31.8 cm.

Explanation / Answer

(a) Area, A = pi*r^2 = pi*0.0306^2 = 2.94166 * 10^-3 m^2 Q = 5.68 * 10^-6 C so, s = Q/A = 1.931 * 10^-3 C/m^2 so, E = 2*pi* (8.99 * 10^9) * (1.931 * 10^-3)* [ 1 - {(3.18 * 10^-3)/((3.06*10^-2)^2 + (3.18*10^-3)^2)^0.5 ] E = 97.7997 * 10^6 N/C (b) with near field approximation, we assume, x x^2 so, x^2 term can be neglected now fraction in brackets becomes:- [ 1 - x/R] as, x

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