PHYSICS / ELECTROMAGNETIC INDUCTION
Calculate signed magnetic flux through a flat area in a uniform magnetic field.
METHOD / WORKED EXAMPLE
Magnetic flux is an oriented field-through-area quantity; using the surface plane instead of its normal creates a sine-versus-cosine error.
WORKED DEFAULT
For B = 0.8 T, area = 0.25 m squared, and a 30-degree field-to-normal angle, flux is 0.8 x 0.25 x cos(30 degrees) = 0.173205 Wb.
READ THE RESULT
Positive or negative flux depends on the chosen area-normal direction. Faraday induction depends on change in linked flux over time, not merely this one static value.
ASSUMPTIONS AND LIMITS
The field is uniform across a flat surface and theta is measured from the chosen surface normal, not from the surface plane.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
COMMON QUESTIONS
No. This equation uses the angle between the magnetic field and the surface's normal vector. A field perpendicular to the surface is parallel to the normal, so theta is zero and flux magnitude is maximum. A field lying in the surface gives ninety degrees and zero flux.
Flux is oriented because the area has a chosen normal direction. Reversing that normal or reversing the field changes the dot-product sign. The sign is meaningful when applying Faraday and Lenz laws, but it does not mean the field strength or physical area itself is negative.
No. It calculates one static flux value through one area. Induced emf requires the rate of change of linked flux and usually the number of turns. Compare flux at defined times or use a time-dependent model, then apply Faraday's law with a consistent orientation convention.
RELATED TOOLS
Use boundary
Evaluate the dot product of a uniform magnetic field with one planar area vector. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
Phi = BA cos(theta)