Disk of Uniform Surface Charge Density Question?

Question

A disk of radius 2.5 cm carries a uniform surface charge density of 3.7 mu or micro CC/m2. Using reasonable approximations, find the magnitude of the electric field on the axis at the following distances.

(a) 0.01 cm

HINT: 0.01 cm is very small compared with the size of the disk. So it may be reasonable to approximate the disk as effectively infinitely large.

(b) 5 m

HINT: 5 m is very large compared with the size of the disk. So it may be reasonable to approximate the disk as effectively pointlike.

Answer 1

Assuming the disk is effectively infinitely large,

but not a charged conducting sheet!

From Gauss's law:

E=d/(2*eo)

eo=8.85*10^-12

a) E=(3.7*10^-6)/(2*8.85*10^-12) = 209,039.55 N/c

**************************************...

Assuming the disk as effectively pointlike.

Assuming the disk's surface area given by:

Compute charge of sheet:

2.5 centimeters = 0.025 meters

area=pi*r^2

area=3.14158*(0.025)^2 = 0.0019634875 m^2

charge of sheet=

Note: "sheet of charge"="one layer"

charge =sheet area * surface charge density

0.0019634875*3.7*10^-6 = 7.265*10^-09 C

**************************************...

From Coulomb's law:

E=k*q/r^2

k=(9*10^9)

b) E=(9*10^9)*(7.265*10^-09)/(5^2) = 2.6154 N/C

hope this helps. If not, more detail ok.