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Date November 2011 Marks available 3 Reference code 11N.2.HL.TZ0.7
Level Higher level Paper Paper 2 Time zone Time zone 0
Command term Draw Question number 7 Adapted from N/A

Question

Part 2 Electromagnetic induction

The diagram shows a horizontal metal rod suspended by two vertical insulated springs.

The rod moves vertically up and down with simple harmonic motion with a time period T at right angles to a uniform magnetic field.

The diagram shows the variation with time t of the vertical displacement x of the rod.

 

On the axes provided, draw a graph to show

(i) the variation with time t of the vertical velocity v of the rod.

(ii) the variation with time t of the emf  generated between the ends of the rod.

[3]
a.

The length of the rod is 0.18 m and the magnitude of the magnetic field is 58 μT. The frequency of the simple harmonic motion is 2.5 Hz. The amplitude of the motion is 8.2×10-2 m.

Determine the magnitude of the maximum emf εmax between the ends of the rod.

[3]
b.

The frequency of the motion is doubled without any change in the amplitude of the motion.

State and explain the changes to the variation with time t of the emf \(\varepsilon \) generated as a result of this change in frequency.

[4]
c.

Markscheme

(i)

cosine wave same frequency as original;
phase correct;

(ii) emf in phase or antiphase with answer to (a)(i);

a.

max speed =8.2×10-2×2π×2.5(=1.29ms-1);
ε=58×10-6×0.18×1.29;
13.5 μV;

b.

frequency of the emf doubles / period halves;
because same change of flux in half the time / because frequency of emf must equal frequency of oscillation;
maximum emf doubles;
maximum speed doubles / flux changes at twice rate;

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Additional higher level (AHL) » Topic 11: Electromagnetic induction » 11.1 – Electromagnetic induction
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