Final answer:
To find the flux linkage for a non-perpendicular surface, calculate the perpendicular component of the area relative to the field and multiply by the field strength. Use the cosine of the angle between the field and the normal to the surface in the flux linkage equation.
Step-by-step explanation:
When finding flux linkage for a surface that is not perpendicular to the magnetic or electric field, you need to consider the component of the area that is perpendicular to the field. The flux (Φ) through a surface inclined at an angle θ is given by the dot product of the field strength (E or B) and the area (A) vector multiplied by the cosine of the angle between them, such that Φ = E · (A cos θ). In the case of an electric field, if Ģ is a unit vector normal to the surface, the flux linkage would be p = E · 1₂ A₂, where the dot represents the dot product and gives the component of the electric field along the unit normal to the surface. Similar principles apply when considering a magnetic field, where the magnetic flux (Φ) would be the product of the magnetic field (B) and the component of the area perpendicular to the magnetic field lines.
For a more intuitive understanding, consider the analogy of a hula hoop in a flowing river; the flow through the hoop represents the flux and it's helpful to remember that only the portion of the area perpendicular to the flow counts for flux calculation. Ultimately, finding the flux through a non-perpendicular surface involves using trigonometry to determine the effective area that interacts with the field lines.