Dalia S.

asked • 09/15/14

Calculate the electric field on the axis of the disk

A uniformly charged disk of radius 35.0 carries charge with a density of 7.90x10-3 C/m2. Calculate the electric field on the axis of the disk at 
(a) 5.00 cm 
(b) 10.0 cm
(c) 50.0 cm 
(d) 200 cm from the center of the disk 

2 Answers By Expert Tutors

By:

Dalia S.

thank you for you explanation, its a bit difficult to imagine the diagram but i think i got a good understanding of it. What would be values for R and z? Would you mind solving (a) so i can see how you go about doing it and i will proceed with the rest of the question. 
You were great help! thank you
Report

09/16/14

Stephen K.

tutor
Dalia,
 
R is the radius of the disk:  R = 35cm = 0.35m and z is the position on the disk axis at which we would like to find the value of the electric field, for part a z = 5 cm = 0.05m  (note that it is important to use meters NOT centimeter to be consistent (your charge density is given in C/m²)
 
k is a constant = 9.0 x 109 N·m²/C²
 
So for (a):
 
Ez = 2π(9.0x109 N·m²⁄C²)(7.90x10-3 C/m²){1-(0.05 m)/[(0.05 m)²+(0.35m)²]½}
 
Ez = 2π(9.0x109 N·m²⁄C²)(7.90x10-3 C/m²)·[1 -  0.05/(.125)½]
 
Ez = 2π(9.0x109 N·m²⁄C²)(7.90x10-3 C/m²)·[1 - 0.35]
 
Ez = 2π(9.0x109 N·m²⁄C²)(7.90x10-3 C/m²)·(0.646)
 
Putting all this together gives:
 
Ez4.47 x 108 N/C (I used Ez to indicate that this is the field in the +z direction)
 
 
 
Report

09/16/14

Dalia S.

in the third step how did you go from [1-0.05/(.125)^1/2] to [1-0.35] in the next step? because what i see you did is simply square 0.125 then substract it from 1 however should you have squared 0.125 then divided it by 0.05 before you subtract it from 1?
Report

09/16/14

Stephen K.

tutor
Dalia, 
 
You are correct, there is an error starting at the 3rd to last line.  That last term should be:
 
1 - (0.05)/(0.125)½ = 1 - 0.1 = 0.86
 
Then the final result will be:  3.84x108
 
Thank you for bringing it to my attention.  Sorry for the confusion, but glad to see you were able to follow along.
Report

09/16/14

Dalia S.

perfect thank you it is much clearer now! i would go about computing b. c and d in the same manner?
Report

09/16/14

Stephen K.

tutor
Simply replace z in the numerator and z2 in the denominator with the values given for b, c, and d.  The only thing that will be changing is z in that [1 - z/(z²+R²)½] term (make sure you change from cm to m though!).
Report

09/16/14

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.