# Finding the charge of a drum, i got the steps i think

#### mr_coffee

The drum of the photocpying machine in problem 16 has a length of 42cm and a diameter of 12cm. What is the total charge on the drum? In problem 16 it says, The e filed just above the surface of the charged drum of a photocopying machine has a magnitude E of 2.3x10^5 N/C. So I first found the charge density $\delta$. E = $\delta$/2PIEor; $\delta$ = E(2PI)(8.85x10^-12)(.006m) = 7.67x10^-8; Then i used $\delta$ = q/Surface Area. q = (2PIrh)$\delta$; q = 2PI(.006m)(.042m)*7.67x10^-8 = 1.21x10^-10 Which is wrong. The book got .32x10^-6C. Any idea where i messsed up at?

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#### geosonel

mr_coffee said:
The drum of the photocpying machine in problem 16 has a length of 42cm and a diameter of 12cm. What is the total charge on the drum? In problem 16 it says, The e filed just above the surface of the charged drum of a photocopying machine has a magnitude E of 2.3x10^5 N/C. So I first found the charge density $\delta$. E = $\delta$/2PIEor; $\delta$ = E(2PI)(8.85x10^-12)(.006m) = 7.67x10^-8; Then i used $\delta$ = q/Surface Area. q = (2PIrh)$\delta$; q = 2PI(.006m)(.042m)*7.67x10^-8 = 1.21x10^-10 Which is wrong. The book got .32x10^-6C. Any idea where i messsed up at?
for a charged cylinder, Gauss's Law yields:

$$E \ = \ \frac{\delta}{2 \pi \epsilon_{0} R}$$

where δ is the charge per unit length. Recalculate your results using the proper δ interpretation. also, the drum length is 0.42 m, and the radius R is 0.06 m. your values for these dimensions are off by a factor of 10!

#### mr_coffee

So i can't use $$E \ = \ \frac{\delta}{2 \pi \epsilon_{0} R}$$ to find the linear charge?

#### geosonel

mr_coffee said:
The drum of the photocpying machine in problem 16 has a length of 42cm and a diameter of 12cm. What is the total charge on the drum? In problem 16 it says, The e filed just above the surface of the charged drum of a photocopying machine has a magnitude E of 2.3x10^5 N/C. So I first found the charge density $\delta$. E = $\delta$/2PIEor; $\delta$ = E(2PI)(8.85x10^-12)(.006m) = 7.67x10^-8; Then i used $\delta$ = q/Surface Area. q = (2PIrh)$\delta$; q = 2PI(.006m)(.042m)*7.67x10^-8 = 1.21x10^-10 Which is wrong. The book got .32x10^-6C. Any idea where i messsed up at?
mr_coffee said:
So i can't use
$$E \ = \ \frac{\delta}{2 \pi \epsilon_{0} R}$$
to find the linear charge?
for a (long) charged cylinder, you CAN and SHOULD use
$$E \ = \ \frac{\delta}{2 \pi \epsilon_{0} R}$$
to determine charge per unit LENGTH (δ) when given values for the other variables......
the problem is that you interpreted δ to be an area charge density in your original solution (see RED terms in your original solution above).

recalculate your results with the proper "linear charge density" interpretation of δ, and also correct your unit errors (see Msg #2), and you'll get the textbook answer.

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#### mr_coffee

I'm confused on what else I could do....
you said, "the problem is that you interpreted δ to be an area charge density in your original solution" How else can u interpret it? I only know $\delta$ = q/Surface Area. I don't see how else u can find the charge without that formula and solve for q. #### geosonel

mr_coffee said:
I'm confused on what else I could do....
you said, "the problem is that you interpreted δ to be an area charge density in your original solution" How else can u interpret it? I only know $\delta$ = q/Surface Area. I don't see how else u can find the charge without that formula and solve for q. (charge per unit LENGTH of cylinder) = δ = (charge on cylinder)/(LENGTH of cylinder)

#### mr_coffee

Thank you~ I finally got part A. PArt b says, The manufacturer wishes to produce a desktop version of the machine. This requires reducing the drunm length to 28cm and the diameter to 8.0cm. The e field at the drum surface must not change. What must be the charge on this new drum? So i used the same formula:

$$E \ = \ \frac{\delta}{2 \pi \epsilon_{0} R}$$
Solved for $$\delta$$ = 8.142x10^-8. I used r = .04m, I kept E the same. Then i used $$\delta$$ = q/length; q = (8.142x10^-8)(.28m); q = 2.3x10^-8, it should be .14x10^-6C. Any idea where i mseed up:?

#### Doc Al

Mentor
mr_coffee said:
Solved for $$\delta$$ = 8.142x10^-8.
Redo that calculation.

#### mr_coffee

Thanks! worked now!

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