Question

Four closed surfaces are shown, each with circular top and bottom faces and curved sides. The areas Atop and Abot of the top and bottom faces and the magnitudes Btop and Bbot of the uniform magnetic fields through the top and bottom faces are given. The fields are perpendicular to the faces and are either inward or outward. Rank the surfaces according to the magnitude of the magnetic flux through the curved sides, greatest first. Surface Atop (m2) Btop (T) Abott (m2 Bbott (T) a 3 8, inward 6 2, outward b 3 2, inward 7. 8, inward с 2 9, outward 2 14, outward d 2 6, inward 4 2, outward

Answer 1

The magnetic flux through a surface is ɸ = A B Cos θ

Where θ is the angle between the normal to the surface and magnetic field. θ= 0⁰ in all the given cases.

For surface A:

Total flux, ɸ = 3 x 8 + 6 x 2 = 30 Wb

For surface B:

Total flux, ɸ = 3 x 2+ 7 x 8 = 62 Wb

For surface C:

Total flux, ɸ = 2 x 9 + 2 x 14 = 46 W

For surface D:

Total flux, ɸ = 2 x 6 - 4 x 2 = 4 Wb

The ranking of the magnitude of magnetic flux ( from greatest to lowest)

B > C > A > D