IB Physics HL D 4 Induction Questions

Practise IB Physics HL D.4 by applying magnetic flux, Faraday’s law, Lenz’s law and induced-emf evidence to moving conductors and coils.

Exam points

calculate magnetic flux, flux linkage and induced emf from field strength, area, orientation, number of turns or changing flux
apply Faraday’s law and Lenz’s law to determine induced-emf magnitude, current direction and energy-transfer consequences
analyse generators, moving conductors, rotating coils and induction graphs using motional-emf, rms or frequency evidence and stated data

Covered syllabus points

D.4.1 (HL)—Magnetic flux D.4.2 (HL)—Faraday’s law D.4.3 (HL)—Motional emf D.4.4 (HL)—Lenz’s law D.4.5 (HL)—Rotating-coil emf D.4.6 (HL)—Rotation frequency and emf

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Study D.4 Induction conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 6]

(a)

A conducting rod of length L is moved with speed v at right angles to a uniform magnetic field of flux density B. The field is directed into the plane of the page.

[ 3 ]

(i)

Show, using Faraday's law or otherwise, that the potential difference, V, established between the ends of the rod is V=v B L.

[ 3 ]

ALTERNATE 1

In time $\Delta t$ , rod moves a distance $v \Delta t$

Flux increases by $B(L v \Delta t)^{}$

«By Faraday» induced emf is the rate of change of flux: $\frac{B L v \Delta t}{\Delta t}$

«=BLv»

ALTERNATE 2

<<From $\varepsilon=-\frac{N \Delta \Phi}{\Delta t} \gg$

Recognition that $\Phi=B A$

Recognition that N = 1

Recognition that $\frac{\Delta A}{\Delta t}=L v \vee$

<<Leading to V=vBL OR $\varepsilon=\mathrm{BLv}>$

ALTERNATE 3

«In steady state» electrons stop drifting and so net force is zero q v B=q E

Substitution of $E=\frac{V}{L}$ to get result

ALT 1: Correct MP2 scores MP1

ALT2:

V and $\varepsilon$ are interchangeable. Ignore negative sign.

[3]

(b)

A coil is rotating in a region of magnetic field with angular speed $12.56 \mathrm{rad} \mathrm{s}^{-1}$ . At t=0, the field is parallel to the surface of the coil.

[ 3 ]

(i)

State the magnetic flux linkage through the coil at t=0.

[ 1 ]

(ii)

Draw, on the axes, a graph to show the variation with time of the induced emf in the loop. (No numbers are required on the vertical axis.)
emf

Figure for Question (ii) — IB Physics HL

[ 2 ]

[Maximum number: 9]

A rod, R , lies perpendicular to a uniform magnetic field B of strength 0.50 T directed into the plane of the page. R is connected to a circuit and the electric current $I_{\mathrm{R}}$ is 2.0 A .

(a)

A small coil of wire of radius 2.0 cm and 20 turns is now located with its centre 10.0 cm from R. The current in R is kept constant at 2.0 A .

[ 7 ]

(i)

Explain why there is no current induced in the coil.

[ 2 ]

the magnetic field produced by the wire $/ \mathrm{I}_{\mathrm{R}}$ is constant.

therefore the «magnetic» flux/field through the coil is constant.

(ii)

The current in R increases at a constant rate from 2.0 A to 10.0 A in 0.5 seconds.

Calculate the emf induced in the coil.

[ 3 ]

$\begin{aligned} \Delta \mathrm{B}=\frac{\mu_{0}}{2 \pi}\left(\frac{10-2}{0.1}\right) \text { OR } 2 \times 10^{-5}-4 \times 10^{-6}=1.6 \times 10^{-5}<\mathrm{T} \gg \Delta \phi=A \Delta \mathrm{~B}=(\pi)\left(0.02^{2}\right)\left(\left(2 \times 10^{-5}\right)-\left(4 x 10^{-6}\right)\right)=2.5 \times 10^{-8}-5.03 \times 10^{-9} =2.01 \times 10^{-8}<\mathrm{Wb}> \varepsilon=\frac{n \Delta \phi}{\Delta t}=\frac{(20)\left(2.01 \times 10^{-8}\right)}{0.5}=8.0 \times 10^{-7}<\mathrm{V} \gg \end{aligned}$

(iii)

Deduce the direction of the current induced in (c)(ii).

[ 2 ]

(b)

The coil is made to rotate such that an emf is induced. The graph shows the variation with time of the emf induced in the coil.

The frequency of rotation is doubled. Draw on the graph the variation with time of the new emf induced.

[ 2 ]

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