# What is the wire's linear charge density from a proton?

## Homework Statement

A proton orbits a long charged wire, making 1.30*10^6 revolutions per second. The radius of the orbit is 1.20cm.

What is the wire's linear charge density?

## Homework Equations

- q E = m w^2 r
- 9*10^9 [2 λ /r] q = m w^2 r

## The Attempt at a Solution

λ = linear charge dens
w = 2pi/period = 2pi/T
w = d theta/dt = 1.4* 2pi /1

I'm confused on how to solve for λ here though. Can anyone help me out?

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You said you know:
F=m v^2/r=m r ω^2=mr(2π/t)^2
F=q E= q 2 k λ/r

You correctly said that you have to set them equal to each other
2qkλ/r=4π^2mr/t^2
You were given r and t. q, k, and m are known physical constants. The only unknown variable is λ. Just solve for it and plug in numbers.

You said you know:
F=m v^2/r=m r ω^2=mr(2π/t)^2
F=q E= q 2 k λ/r

You correctly said that you have to set them equal to each other
2qkλ/r=4π^2mr/t^2
You were given r and t. q, k, and m are known physical constants. The only unknown variable is λ. Just solve for it and plug in numbers.
Ah, okay, so I have it set up like this:

(2*1.6*10^-19*9*10^9*λ)/(.012)=(4π^2*1.67*10^-27*.012)/(1.30*10^6)^2

I got 1.95056*10^-33 nC/m but that seems to be wrong, anywhere I went wrong?

Last edited:
Don't plug in numbers until the final answer. Solve for λ, then plug in numbers. Also, just because it's small doesn't mean it's wrong.

Don't plug in numbers until the final answer. Solve for λ, then plug in numbers. Also, just because it's small doesn't mean it's wrong.

Alright so I got λ = 2π^2mr^2/kqt^2. I plugged in the numbers and got the same answer as before though, lol.

Ok, you got the same answer. Why did you think it was wrong?

Ok, you got the same answer. Why did you think it was wrong?
I submitted it through Mastering Physics and it said it was wrong, lol. I'm not sure if its the units because the answer is suppose to be in nC/m, but I am pretty sure it cancels out accordingly. Hmm..

I see the problem. You weren't given the period, you were given the rotation speed. "1.30*10^6 revolutions per second"

I see the problem. You weren't given the period, you were given the rotation speed. "1.30*10^6 revolutions per second"
Oh, so I have to convert the rotation speed to its period? So it would be 1/1300000?

Or you could use the frequency 1.6*10^6 instead of 1/period. Either way, you're multiplying by (1.3*10^6)^2 instead of dividing.

Or you could use the frequency 1.6*10^6 instead of 1/period. Either way, you're multiplying by (1.3*10^6)^2 instead of dividing.
Hmm I got 5.57*10^-33 and that still seems to be wrong, lol.

Let's go back to the equation that you found:
$$\lambda = \frac{2\pi^2mr^2}{kqt^2}$$
Replace t by 1/f to get
$$\lambda = \frac{2\pi^2mr^2f^2}{kq}.$$
Now, what you have been plugging in as t (1.6*10^6s) isn't t, it's the frequency f (1.6*10^6 Hz). Also, make sure that when you're plugging in units, you're using only base units. Only m should be in kg, r should be in m, f should be in Hz, k should be in N*m^2/C^2. Your answer should be in C/m.

Let's go back to the equation that you found:
$$\lambda = \frac{2\pi^2mr^2}{kqt^2}$$
Replace t by 1/f to get
$$\lambda = \frac{2\pi^2mr^2f^2}{kq}.$$
Now, what you have been plugging in as t (1.6*10^6s) isn't t, it's the frequency f (1.6*10^6 Hz). Also, make sure that when you're plugging in units, you're using only base units. Only m should be in kg, r should be in m, f should be in Hz, k should be in N*m^2/C^2. Your answer should be in C/m.
Alright I got 8.439 nC/m and that is still wrong, lol. Damn, I don't know where I'm going wrong. I'm plugging in everything:

I got:
m = 1.67*10^-27 kg
r = .012m
f = 1.6*10^6 Hz
k = 9*10^9 N*m^2/C^2
q = 1.6*10^-19 C

That's because I had a typo and I wrote 1.6 MHz instead of 1.3 MHz.

That's because I had a typo and I wrote 1.6 MHz instead of 1.3 MHz.
Ah, I finally got it. Thanks alot for all of your help, I really appreciate it.

You're welcome.