- #1
horsewnoname
Homework Statement
An infinitely long wire carries current [itex]I=I_0sin(wt)[/itex]. A distance [itex]a[/itex] from this wire is an [itex]w[/itex] by [itex]l[/itex] loop with resistance [itex]R[/itex] with induced voltage [itex]V[/itex] and induced current [itex]i[/itex]. Find the induced voltage and current in the loop.
Homework Equations
Faraday's law is given by [itex]\varepsilon = \oint \mathbf{E}\cdot d\mathbf{l}=-\frac{d\phi }{dt}[/itex]where [itex]\phi[/itex] is the magnetic flux given by [itex]\int \boldsymbol{B}\cdot d\boldsymbol{s}[/itex].
The Attempt at a Solution
I know that in order to find the voltage, I need to find the emf which is given by Faraday's law stated above. I pursue this by first coming up with an expression for the magnetic flux.
Although, to do this, I first need to know the magnetic field produced by the infinite wire. From memory (or by Ampere's law), I know this to be [itex]B=\frac{\mu _0I}{2\pi r}[/itex].
The problem I am having is that the magnetic field is a function of [itex]r[/itex] which bothers me. When I use this magnetic field expression to determine the flux and then take the derivative with respect to time to yield the emf, the result is an expression for the voltage that varies with [itex]r[/itex] which makes no sense. What am I forgetting?