Flux and flux linkage passing through a rectangular coil rotated in a…

The idea

Magnetic flux density B measures field strength in tesla (T). Magnetic flux Φ through an area A is Φ = BAcosθ, where θ is the angle between the field direction and the normal to the coil area. For a rectangular coil of N turns, flux linkage is NΦ = BANcosθ. In Required practical 11, a search coil connected to an oscilloscope is placed in an alternating magnetic field produced by a larger coil. The AC field causes a continuously changing flux linkage, inducing an alternating e.m.f. in the stationary search coil. By varying the angle θ between the search coil's normal and the field, the peak-to-peak induced voltage changes. The trace amplitude is proportional to the maximum flux linkage, demonstrating the cosine relationship.

What earns the marks

• State that magnetic flux Φ is the product of flux density and the area perpendicular to the field, Φ = BAcosθ, with θ measured between the field direction and the normal to the coil.
• For a coil of N turns, define flux linkage as NΦ and derive NΦ = BANcosθ, identifying B, A, N and θ with correct units: T, m², dimensionless and degrees or radians.
• Explain that in an alternating magnetic field, the flux linkage varies continuously, inducing an e.m.f. proportional to the rate of change of flux linkage.
• Describe Required practical 11: place a search coil in an alternating magnetic field, connect it to an oscilloscope, vary the angle between the coil normal and the field, and record the peak induced voltage.
• Interpret the oscilloscope trace: the amplitude of the induced AC voltage is directly proportional to the maximum flux linkage at that angle.
• Use a data table or graph of induced voltage against angle or against cosθ to identify the relationship between orientation and flux linkage, recognising sources of uncertainty such as imperfect alignment.

Common mistakes and how to put them right

• Measuring θ from the plane of the coil instead of from the normal to the coil.

  Put it right by defining θ as the angle between the field direction and the normal.

• Treating flux linkage as a vector or adding N and A incorrectly.

  Put it right by using the scalar product NΦ = BANcosθ and checking that the units reduce to weber-turns.

• Assuming the search coil must be rotated continuously to get a trace.

  Put it right by explaining that the alternating field provides the changing flux, so a stationary coil at a fixed angle produces a steady AC trace.

Exam tips

• Sketch the coil, field lines and normal clearly, label θ at the normal, and write NΦ = BANcosθ before substituting values.
• When describing Required practical 11, state the independent variable (angle), dependent variable (oscilloscope voltage amplitude) and control variables such as AC frequency and primary coil current.
• Link any oscilloscope observation to Faraday's law by stating that e.m.f. is proportional to the rate of change of flux linkage.