- #1
space-time
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Sorry I couldn't finish the title. I ran out of space. Anyway, here's the question:
A uniformly charged, infinitely long line of negative charge has a linear charge density of -λ and is located on the z axis. A small positively charged particle that has a mass m and a charge q is in circular orbit of radius R in the xy plane centered on the line of charge. (Use the following as necessary: k, q, m, R, and λ.)
(a) Derive an expression for the speed of the particle.
(b) Obtain an expression for the period of the particle's orbit.
Relevant Equations:
E = λ/(2πrε0) for an infinite line of charge. In the case of this problem I used -λ instead of just λ.
F = Eq = mv2/r
T = (2π)/ω = (2π)/(v/r) = (2πr)/vI tried using the first equation I listed above in order to derive E. This led to:
E = -λ/(2πRε0)
F = Eq = mv2/R , so this leads to:
F = -λq/(2πRε0) = mv2/R
solving algebraically for v yields:
v = sqrt(-λq/(2πmε0)) = sqrt(-λkq / (2m) )
Here I thought I had derived v, but webassign said that this was wrong. I tried taking out the negative sign since having an imaginary velocity makes no sense, but it was still wrong. I can't do (b) until I solve (a). Please help.
A uniformly charged, infinitely long line of negative charge has a linear charge density of -λ and is located on the z axis. A small positively charged particle that has a mass m and a charge q is in circular orbit of radius R in the xy plane centered on the line of charge. (Use the following as necessary: k, q, m, R, and λ.)
(a) Derive an expression for the speed of the particle.
(b) Obtain an expression for the period of the particle's orbit.
Relevant Equations:
E = λ/(2πrε0) for an infinite line of charge. In the case of this problem I used -λ instead of just λ.
F = Eq = mv2/r
T = (2π)/ω = (2π)/(v/r) = (2πr)/vI tried using the first equation I listed above in order to derive E. This led to:
E = -λ/(2πRε0)
F = Eq = mv2/R , so this leads to:
F = -λq/(2πRε0) = mv2/R
solving algebraically for v yields:
v = sqrt(-λq/(2πmε0)) = sqrt(-λkq / (2m) )
Here I thought I had derived v, but webassign said that this was wrong. I tried taking out the negative sign since having an imaginary velocity makes no sense, but it was still wrong. I can't do (b) until I solve (a). Please help.