Electromagnetic Induction | Class 12 Physics Notes

6.3 MAGNETIC FLUX

Magnetic flux (Φ_B) is a quantitative measure of the magnetic field passing through a given surface area. It is defined analogously to electric flux. For a plane surface of area A placed in a uniform magnetic field B, the magnetic flux is given by the dot product of the magnetic field vector and the area vector: Φ_B = B · A = B A cos θ, where θ is the angle between the magnetic field vector and the normal to the surface (area vector). The area vector is perpendicular to the surface, with magnitude equal to the area.

For non-uniform magnetic fields or curved surfaces, the total magnetic flux is obtained by dividing the surface into infinitesimal elements dA, calculating the flux through each element, and summing (integrating) over the entire surface: Φ_B = Σ B_i · dA_i. The SI unit of magnetic flux is the weber (Wb), equivalent to tesla meter squared (T m²). Magnetic flux is a scalar quantity, despite being defined via a vector dot product, because it represents a scalar measure of the total magnetic field passing through the surface.

Understanding magnetic flux is crucial because changes in magnetic flux through a circuit induce an emf, as will be discussed in Faraday's law. The flux depends on the magnitude of the magnetic field, the area of the surface, and the orientation of the surface relative to the field.

📊 Diagram: See figure_5: FIGURE 6.4 A plane of surface area A placed in a uniform magnetic field B; figure_6: FIGURE 6.5 Magnetic field B1 at the ith area element. dA1 represents area vector of the ith area element.

🧪 Activity: Calculating magnetic flux through various surfaces and understanding dependence on orientation and field strength.

🔗 Connection: This section introduces magnetic flux, which is essential for stating and understanding Faraday's law of induction in the next section.