Dalia S.

# 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
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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)

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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?
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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.
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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?
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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!).
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09/16/14

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