AQA A-Level Physics: Magnetic Fields, Induction and AC

A student holds a vertical hollow plastic tube and drops a small bar magnet so that it falls straight down through a flat coil of insulated copper wire wound around the middle of the tube. The two ends of the coil are connected to a sensitive datalogger that records the EMF induced across the coil. As the magnet falls through the coil the datalogger shows a voltage that rises to a positive peak, returns to zero, then swings to a negative peak of larger magnitude.

Explain, using the laws of electromagnetic induction, why an EMF is induced as the magnet falls through the coil, why the two peaks point in opposite directions, and why the second (lower) peak is larger in magnitude than the first. Refer to Faraday's law and Lenz's law in your answer.

(6 marks)

In a particle-physics demonstration, a beam of protons enters a region of uniform magnetic field at right angles to the field. The magnetic field causes each proton to travel in a circular arc. The measured values are given below.

Quantity	Value
Magnetic flux density, $B$B	0.85 T
Radius of the circular path, $r$r	0.072 m
Charge on a proton, $Q$Q	$1.60 \times 10^{-19}$1.60×10−19 C
Mass of a proton, $m$m	$1.67 \times 10^{-27}$1.67×10−27 kg

(a) Explain why the protons follow a circular path rather than a path that curves through and then straightens out. (2 marks)

(b) Calculate the speed of the protons as they travel along the arc. (2 marks)

(c) Hence calculate the kinetic energy of one proton, in joules. (2 marks)

A coil is placed near an electromagnet whose current is being changed by an operator. A datalogger records the magnetic flux linkage $N\Phi$NΦ through the coil at regular time intervals. The recorded values are shown below.

Time / s	0	0.10	0.20	0.30	0.40
Flux linkage, $N\Phi$NΦ / Wb turns	0	0.0080	0.0240	0.0300	0.0300

(a) State the relationship, in words, between the induced EMF in the coil and the flux-linkage data in the table. (1 mark)

(b) Calculate the magnitude of the induced EMF during the interval from 0 to 0.10 s and during the interval from 0.10 s to 0.20 s. (2 marks)

(c) State during which 0.10 s interval the induced EMF is greatest and during which interval it is zero, and explain your two answers by reference to the data. (2 marks)

A power station generates electrical power at an output of 25 MW and a voltage of 25 kV. This is fed into the primary coil of an ideal step-up transformer before transmission along a cable to a distant town. The transformer and cable details are given below.

Quantity	Value
Output power of station, $P$P	25 MW
Primary (input) voltage, $V_p$Vp​	25 kV
Turns on the primary coil, $N_p$Np​	500
Turns on the secondary coil, $N_s$Ns​	8000
Total resistance of the transmission cable, $R$R	8.0 Ω

Assume the transformer is 100% efficient.

(a) Calculate the secondary (transmission) voltage produced by the transformer. (2 marks)

(b) Calculate the current in the transmission cable. (1 mark)

(c) Calculate the power dissipated in the transmission cable, and state what this calculation shows about the advantage of transmitting power at a high voltage. (2 marks)

A domestic immersion heater contains a resistive element of resistance 53 Ω. It is connected to an alternating mains supply whose root-mean-square (rms) voltage is 230 V.

(a) Calculate the peak voltage $V_0$V0​ of the supply. (2 marks)

(b) Calculate the mean (average) power dissipated by the heating element. (2 marks)

A straight wire carrying a current is placed at right angles to a uniform magnetic field and experiences a force (the motor effect). The direction of this force can be predicted using Fleming's left-hand rule.

State what each of the three mutually perpendicular directions (the thumb and the first and second fingers) represents in Fleming's left-hand rule, and state one condition that must hold for the wire to experience the maximum force. (3 marks)