Which expression gives magnetic flux?

1. Analyze the question You are asked which expression gives magnetic flux (Φ). Each option is a different electromagnetism formula, so you need to match each one to what it actually represents.

2. Explain the concept Magnetic flux is a measure of how much magnetic field passes through a surface. For a uniform field B passing through an area A:

Φ = BA cos θ

Here θ is the angle between the magnetic field B and the normal (the perpendicular) to the surface. The unit is the weber (Wb), where 1 Wb = 1 T·m².

3. Check each option

• A. qVB sin θ: This is the magnetic force on a moving charge (F = qvB sin θ). It is not flux.
• B. μφI/(2πr): This resembles the magnetic field around a long straight wire, B = μI/(2πr). It is a field strength, not flux. (The extra φ looks like a typo anyway.)
• C. BA cos θ: This is the magnetic flux, Φ = BA cos θ. ✔
• D. −N dΦ/dt: This is Faraday's law of induced emf, ε = −N(dΦ/dt). It is the rate of change of flux linkage, not flux itself.

4. Answer The correct option is C. BA cos θ.

5. Exam tip Remember the "flux family" this way:

• Flux: Φ = BA cos θ (the Wb)
• Induced emf: ε = −N dΦ/dt (the rate of change of flux)
• Force on a charge: F = qvB sin θ (sin for force, cos for flux)

Also, if the field is perpendicular to the surface (θ = 0°), flux is maximum, Φ = BA. If the field is parallel to the surface (θ = 90°), flux is zero.