How can a constant magnetic field in a coil lead to an increasing induced EMF?

[syang9]

induced emf!

Hello,

I am studying magnetic induction, induced emf, and faraday's law, that sort of thing. My book gives an example where the magnitude of a B-field is increasing at constant rate through an axis of a circular coil with N number of turns and a certain radius r, find the induced emf in the coil. However, in the solution, it says that the B-field is constant, and can be removed from the flux integral! How can this be possible, if it is increasing with time?

Thanks,

Stephen

 

[OlderDan]

Hello,

I am studying magnetic induction, induced emf, and faraday's law, that sort of thing. My book gives an example where the magnitude of a B-field is increasing at constant rate through an axis of a circular coil with N number of turns and a certain radius r, find the induced emf in the coil. However, in the solution, it says that the B-field is constant, and can be removed from the flux integral! How can this be possible, if it is increasing with time?

Thanks,

Stephen

The flux integral is an integral over an area at each moment in time. If the magnetic field is the same throughout the area enclosed by the coil, it is a constant for that integral. The result of the calculation will be a flux that depends on time. The rate of change of that flux with time gives you the induced emf.

 

[OlderDan]

Hello,

I am studying magnetic induction, induced emf, and faraday's law, that sort of thing. My book gives an example where the magnitude of a B-field is increasing at constant rate through an axis of a circular coil with N number of turns and a certain radius r, find the induced emf in the coil. However, in the solution, it says that the B-field is constant, and can be removed from the flux integral! How can this be possible, if it is increasing with time?

Thanks,

Stephen

The flux is the integral of the magnetic field over an area at each moment in time. If the magnetic field is the same throughout the area enclosed by the coil, it is a constant for this integral. The result of the calculation will be a flux that depends on time. The rate of change of that flux with time gives you the induced emf.