Magnetic Flux Through a Surface

Identify B, A, and the correct angle with the area vector. Convert units to tesla and square metre. Substitute in Phi_B = BA cos theta. State the answer in weber and mention whether flux is maximum, reduced, or zero.

A useful diagram shows a flat loop, magnetic field lines, the normal to the loop as the area vector A, and the angle theta between B and A. Marking theta with the plane instead of the normal causes wrong answers.

Using sin theta directly because the angle is given with the plane, or writing the SI unit as tesla metre instead of weber.

Magnetic flux through a surface is the measure of the magnetic field passing normally through that surface. For a uniform magnetic field, it is given by Phi_B = B A cos theta.

Magnetic flux through a surface is the measure of the magnetic field passing normally through that surface. For a uniform magnetic field, it is given by Phi_B = B A cos theta. Formula: Phi_B = B A cos theta. Here Phi_B is magnetic flux in weber (Wb), B is the magnetic field or magnetic flux density in tesla (T), A is the surface area in square metre (m^2), and theta is the angle between B and the area vector, not the plane of the coil. The term B cos theta is the component of magnetic field normal to the surface, so the formula measures only the field crossing the surface normally. If a coil is kept with its plane perpendicular to a magnetic field, its area vector is parallel to the field, so theta = 0 degrees and flux is maximum: Phi_B = BA.

Magnetic flux depends on three things: magnetic field strength B, area A, and the angle theta between the magnetic field and the area vector. The area vector is perpendicular to the surface. Flux is maximum when the field is perpendicular to the surface and zero when the field is parallel to the surface. Formula: Phi_B = B A cos theta. Here Phi_B is magnetic flux in weber (Wb), B is the magnetic field or magnetic flux density in tesla (T), A is the surface area in square metre (m^2), and theta is the angle between B and the area vector, not the plane of the coil. The term B cos theta is the component of magnetic field normal to the surface, so the formula measures only the field crossing the surface normally. A circular coil of area 0.020 m^2 is placed in a uniform magnetic field of 0.50 T. If the area vector makes an angle of 60 degrees with the field, Phi_B = B A cos theta = 0.50 x 0.020 x cos 60 degrees = 0.010 x 0.5 = 0.005 Wb. The flux linked with the coil is 5.0 x 10^-3 Wb. Questions may ask for flux calculation, maximum or zero flux condition, unit of flux, or the effect of rotating a coil in a magnetic field. Using sin theta directly because the angle is given with the plane, or writing the SI unit as tesla metre instead of weber.