Electric Field and the Speed of a Proton

In summary, the conversation discusses the calculation of the speed of a proton moving in a circular orbit just outside a spherical shell with a charge of -60.0 nC at its center. After some calculations and adjustments, the correct answer is found to be on the order of 10^5, rather than the initially calculated value of 10^12, which is faster than the speed of light.
  • #1
Ithryndil
142
0

Homework Statement


A particle with a charge of -60.0 nC is placed at the center of a nonconducting spherical shell of inner radius 20.0 cm and outer radius 34.0 cm. The spherical shell carries charge with a uniform density of -2.26 µC/m3. A proton moves in a circular orbit just outside the spherical shell. Calculate the speed of the proton.

Homework Equations


We will need:
[tex]E = F/q_{o}[/tex]
[tex]\Phi=EA=q_{inside}/\epsilon_{o}[/tex] (no integral is needed because we know the electric field will be constant at the surface of the sphere and we know the surface area of a sphere).
[tex] F = ma_{c}[/tex]

The Attempt at a Solution



Solving for E I get:

E = [tex]q_{inside}/(\epsilon_{o}A)[/tex]

[tex]q_{o}[/tex] is just the inner charge (-60.0nC) + the outer charge [4/3*pi*charge density*(0.34^3-0.20^3).

Plugging in for E I get:

[tex]F/q_{o}=q_{inside}/(\epsilon_{o}A)[/tex]

[tex]q_{o} = q_{inside}[/tex] because the spherical surface should act as a point charge right?

Therefore after some algebra and substitution for the centripetal acceleration I get:

[tex] v = \sqrt{q^{2}/(4\pi\epsilon_{0}rm})[/tex]
Where r = .34 and m is the mass of a proton.

When I plug in all the values I get a speed on the order of [tex]10^{12}m/s[/tex]
Which is faster than the speed of light if I am not mistaking...that being roughly [tex]3 x 10^{8}m/s[/tex]

What am I doing wrong?
 
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  • #2
Ithryndil said:

Homework Statement

[tex]F/q_{o}=q_{inside}/(\epsilon_{o}A)[/tex]

[tex]q_{o} = q_{inside}[/tex] because the spherical surface should act as a point charge right?

My problem lies with the above. [tex]q_{o} = q_{inside}[/tex]. That is a false statement. The [tex]q_{o}[/tex] is actually the charge of the proton, not the charge of the entire charge configuration. With that adjustment I get an answer on the order of 10^5 which is must more realistic and was the correct answer.
 
  • #3
Yup that's right. Good that you figured it out by yourself.
 

1. What is an electric field?

An electric field is a region in which an electric charge experiences a force. It is created by a source charge and extends in all directions, exerting a force on any other charged particle that enters the field.

2. How is the electric field strength related to the speed of a proton?

The electric field strength is directly proportional to the speed of a proton. This means that as the electric field strength increases, the speed of the proton also increases, and vice versa.

3. How is the speed of a proton affected by the direction of the electric field?

The speed of a proton is affected by the direction of the electric field. If the electric field is in the same direction as the proton's motion, the proton will speed up. If the electric field is in the opposite direction, the proton will slow down.

4. Can the speed of a proton be calculated using the electric field strength?

Yes, the speed of a proton can be calculated using the electric field strength. This can be done using the equation: F = qE, where F is the force on the proton, q is the charge of the proton, and E is the electric field strength.

5. How can the speed of a proton be manipulated using the electric field?

The speed of a proton can be manipulated by changing the electric field strength. By increasing or decreasing the electric field strength, the force on the proton will change, resulting in a change in the proton's speed. Additionally, changing the direction of the electric field can also affect the proton's speed.

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