- #1
peripatein
- 880
- 0
Hi,
A system, with cylindrical symmetry and charge density ρ(r) = ρ0e-r2/a2, where a is a given constant, is given.
The system moves at a constant velocity V in the z^ direction. V<<c. The charge density in the lab's reference frame is approx. equal to that in the rest reference frame.
I am asked for the electrical and magnetic fields (magnitude and direction) everywhere.
I have managed to find the electrical field to be equal (2πρ0a2/r)*(1 - e-r2/a2) r^. I have confirmed that my answer is correct.
Now, what I don't quite understand is why couldn't I equate Lorentz force to zero ("constant velocity") in order to find the magnetic field? This would yield (2πa2ρ0/r)*(c/V)*(1 - e-r2/a2) [itex]\varphi[/itex]^, whereas the correct answer, as asserted by the book, is (2πa2ρ0/r)*(V/c)*(1 - e-r2/a2) [itex]\varphi[/itex]^!
What is the reason for this discrepancy?
By using Ampere's Law, I was able to solve it correctly, yet would like to understand why couldn't I simply have applied the requisite condition on Lorentz force to find the magnetic field?
I'd truly appreciate your help.
Homework Statement
A system, with cylindrical symmetry and charge density ρ(r) = ρ0e-r2/a2, where a is a given constant, is given.
The system moves at a constant velocity V in the z^ direction. V<<c. The charge density in the lab's reference frame is approx. equal to that in the rest reference frame.
I am asked for the electrical and magnetic fields (magnitude and direction) everywhere.
Homework Equations
The Attempt at a Solution
I have managed to find the electrical field to be equal (2πρ0a2/r)*(1 - e-r2/a2) r^. I have confirmed that my answer is correct.
Now, what I don't quite understand is why couldn't I equate Lorentz force to zero ("constant velocity") in order to find the magnetic field? This would yield (2πa2ρ0/r)*(c/V)*(1 - e-r2/a2) [itex]\varphi[/itex]^, whereas the correct answer, as asserted by the book, is (2πa2ρ0/r)*(V/c)*(1 - e-r2/a2) [itex]\varphi[/itex]^!
What is the reason for this discrepancy?
By using Ampere's Law, I was able to solve it correctly, yet would like to understand why couldn't I simply have applied the requisite condition on Lorentz force to find the magnetic field?
I'd truly appreciate your help.