Re: [Phys-l] Question about Electromagnetic Induction

[John Denker <jsd@av8n.com>]

On 04/06/2009 10:44 AM, Fakhruddin, Hasan wrote:

> Consider a circular conducting loop of radius 'a'.  Concentric and
> coplanar to it is a circle of radius 'b' (b<a) within which there is
> uniform magnetic field perpendicular to the plane of the conducting
> loop.  The magnetic field is varying at a rate dB/dt.
>
> QUESTION:  Does the induced emf in the loop depend on the radius 'a'?
> If not, then can the radius 'a' take larger values without limit?

The question is ill-posed, because it doesn't specify what
the field is doing outside radius b.

I will assume that the intent was for the field to be zero
at all points outside radius b and inside some larger radius
Zmax.  (If this is not what was intended, please clarify.)

Subject to this assumption, the induced voltage in loop a is
independent of radius for all a in the range from b to Zmax.
This is one of the Maxwell equations:  Voltage = flux dot.

You cannot increase a without limit;  it is limited by Zmax,
which cannot be infinite, because magnetic field lines are
endless.  The return flux has to go _somewhere_.  You can
engineer it to lie outside Zmax, but you cannot push it to
infinity.