Magnetic flux and flux linkageAQA A-Level Physics: Subtopic test

1. 1
   A flat circular coil of 200 turns and radius 3.0 cm is placed in a uniform magnetic field of flux density 0.040 T, with the plane of the coil perpendicular to the field direction.

   (a)

   What is the magnetic flux through one turn of the coil?

   [1 mark]

   • A3.6 × 10⁻⁵ Wb
   • B2.3 × 10⁻² Wb
   • C3.8 × 10⁻³ Wb
   • D1.1 × 10⁻⁴ Wb

   (b)

   Which of the following is equivalent to the unit weber?

   [1 mark]

   • AT m⁻²
   • BT m
   • CT m²
   • DT s

   (c)

   The coil is turned so that the normal to its plane makes an angle of 60° with the field. Calculate the flux linkage.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student uses a small search coil connected to an oscilloscope to investigate how the magnetic flux linkage depends on orientation. The search coil is placed inside a long solenoid carrying a low-frequency alternating current from a signal generator. The search coil can be rotated so that the angle θ between its axis (the normal to its plane) and the field direction can be set to chosen values. For a fixed frequency, the peak-to-peak height of the oscilloscope trace is taken to be proportional to the peak flux linkage.

   (a)

   Why must the solenoid current be alternating rather than steady?

   [1 mark]

   • AAn emf is induced in the search coil only when its flux linkage changes
   • BA steady current would heat the search coil
   • CAn oscilloscope cannot display a steady voltage
   • DA steady current produces no magnetic field

   (b)

   Which graph should give a straight line through the origin?

   [1 mark]

   • APeak-to-peak height against θ
   • BPeak-to-peak height against cos θ
   • CPeak-to-peak height against sin θ
   • DPeak-to-peak height against 1/θ

   (c)

   With θ = 0° the peak-to-peak height is 48 mm. Predict the height when θ = 40°.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A rectangular coil of 150 turns measures 8.0 cm by 5.0 cm. It is placed in a uniform magnetic field of flux density 0.12 T.

   (a)

   Calculate the flux linkage when the plane of the coil is perpendicular to the field, and when the plane of the coil makes an angle of 30° with the field direction.

   [3 marks]

   (b)

   The coil is rotated uniformly at 25 revolutions per second about an axis in its plane and at right angles to the field. At t = 0 its plane is perpendicular to the field. Calculate the flux linkage at t = 7.0 ms.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student wants to confirm that the magnetic flux linkage of a coil varies with the angle θ between the normal to its plane and the field direction as NΦ = BAN cos θ. A search coil is placed in the uniform alternating field inside a long solenoid driven by a signal generator, and the peak-to-peak height of the trace on a calibrated oscilloscope is taken as proportional to the flux linkage.

   (a)

   Describe how the student should carry out the investigation and process the results to confirm the relationship, and state one source of uncertainty.

   [6 marks]

   (b)

   The student records peak-to-peak heights of 4.8 cm at θ = 0°, 4.2 cm at 30°, 2.5 cm at 60° and 0.2 cm at 90°. Evaluate whether the results support the relationship, and suggest an explanation for the reading at 90°.

   [6 marks]

   Total for question 4: 12 marks

End of questions