Hi Toutsop Zangho Franck Borel

since there are at least two basic possibilities for the direction of dipole axis of the magnets (axial or radial) and three basic possibilities for the direction of the rotation vector (axial, radial and parallel to the dipole axis, radial and perpendicular to the dipole axis), and countless combinations of these directions, the could you please give us a rough sketch of the setup?

Hi Toutsop Zangho Franck Borel

I guess that the circular disc represents the cross-section of the pipe, i. e. the axis of the pipe is parallel to the coordinate axis beta. The two black rectangles are the magnets, and from the direction of the vector V (and the other vector located at the second magnet) I take it that the axis of rotation is parallel to the axis of the pipe, i. e. the angle beta is changing with time, and the angle theta remains constant. Is this correct?

Before going into details of the magnetic field, my guessing goes one step further: I feel that you intend to have some kind of effect of the changing magnetic field on the coil outside the pipe. Suppose the axial component of the coil can be neglected, e. g. because the coil is composed of two layers of winding, with the two terminals located in close neighborhood; then the only effect (induction of a voltage) on a single loop of the coil depends on the temporal changing of the beta-component of the magnetic flux, and the effect on the whole coil depends on the integral of this beta-component taken from one end of the coil to the other end.

It follows that with the axis of rotation parallel to the axis of the coil, there is no effect at all.

Please correct me if I misunderstood your drawing.

Hello Toutsop Zangho Franck Borel

the Biot-Savart law describes the dependence of the magnetic flux density B on electric currents.

If the surface of a permanent magnet contains two opposite planes which represent the poles, then the remaining surface can be treated like a one-layer-coil of identical shape. After deciding how many turns the coil has, you can calculate B at the center of one pole for a unit DC current by using the Biot-Savart law. Next you have to adjust the current in such a way that B equals the actual B of the permanent magnet (that's easy because B depends linearly on the current).

Based on the adjusted current you can numerically determine B at any point in space as long as this point is not located on the coil. The contributions of the two magnets just add vectorially.

To determine the magnetic flux through one of the rings of the coil on the pipe, you have to integrate the component of B which is perpendicular to the plane limited by the ring, over this plane. I feel that solving all integrals involved here is not possible; instead, you'll have to rely on numerical integration. I expect a sinoidal change of the flux over time. If you calculate the flux for, say, 30° steps of the rotating magnets, you will be able determine amplitude and phase of the flux based on your results.

Hi Toutsop Zangho Franck Borel

If it doesn't fit your way of thinking, please get in touch again.