- #1
Ithryndil
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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?