Physics · Electromagnetic Induction · NEET
Always from the NORMAL — the imaginary arrow that points straight out of the flat loop. This is the single most common mistake. If a question gives you the angle with the PLANE, convert it: angle with normal = 90° minus angle with plane. So if B makes 30° with the plane, it makes 60° with the normal, and you use cos 60° = 0.5.
θ = 0°, so cosθ = 1 and flux is MAXIMUM (Φ = BA). If the plane is perpendicular to B, the normal is parallel to B, so the angle between them is zero. NEET 2022 tested exactly this wording: 'plane perpendicular to B' gave Φ = BA, not zero.
Flux is zero when the loop's PLANE is PARALLEL to B (field lines slide along the surface and none pass through). Then the normal is perpendicular to B, θ = 90°, cos 90° = 0, so Φ = 0. Do not confuse 'plane parallel to B' (flux = 0) with 'plane perpendicular to B' (flux = max).
A is the flat area enclosed by the loop, in square metres. For a square of side L, A = L². For a circle of radius r, A = πr². If there are N turns, each turn has the same area A — flux per turn is still BA cosθ; you multiply by N only later in the EMF or flux-linkage formula (NΦ).
Then Φ = BA cosθ only works for the part where B is present. A classic trap: a loop bigger than the field region encloses flux only over the FIELD's area, not the loop's area. Use the area where the field actually exists (πr² of the field patch), not the loop's larger area.
A square loop of side 1 m and resistance 1 Ω is placed in a magnetic field of 0.5 T. If the plane of the loop is perpendicular to the direction of the magnetic field, the magnetic flux through the loop is:
A 800 turn coil of effective area 0.05 m² is kept perpendicular to a magnetic field 5 × 10⁻⁵ T. When the plane of the coil is rotated by 90° about one of its coplanar axes in 0.1 s, the emf induced in the coil will be:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The weber (Wb). From Φ = BA cosθ, unit = tesla × metre² = T·m² = Wb. One weber is one tesla times one square metre.
You may point the normal either way out of the loop; cosθ then differs only in sign. For magnitude of flux (as NEET asks), take the acute angle so cosθ is positive. The sign matters only when you later track the DIRECTION of induced EMF using Lenz's law.
Yes. B·A is the vector dot product of the field and the area vector (area vector points along the normal, magnitude A). The dot product equals BA cosθ, so both forms are identical.
Flux Φ = BA cosθ is for a single turn. Flux linkage is NΦ for N turns. You use flux linkage (NΦ) in EMF and inductance formulas, but the basic Φ = BA cosθ describes just one loop.
Almost every EMI numerical starts by computing flux with Φ = BA cosθ. Faraday's law (EMF = −N dΦ/dt), AC generators, and inductance all build on it. Getting θ right (normal vs plane) is the single biggest source of lost marks in this chapter.
