Topic: Magnetic Fields and Effects of Current …getthosegrades.com/wp-content/uploads/2018/08/Magnetic...The diagram shows a horizontal conductor of length 50 mm carrying a current

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Topic: Magnetic Fields and Effects of Current Specification reference: 3.5.5

Marks available: 63 Time allowed (minutes): 81 Examination questions from AQA. Don’t forget your data sheet! Mark scheme begins on page

Q1. (a) State, in words, the two laws of electromagnetic induction.

Law 1 _____________________________________________________________

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Law 2 _____________________________________________________________

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(3)

(b) The diagram below illustrates the main components of one type of electromagnetic braking system. A metal disc is attached to the rotating axle of a vehicle. An electromagnet is mounted with its pole pieces placed either side of the rotating disc, but not touching it. When the brakes are applied, a direct current is passed through the coil of the electromagnet and the disc slows down.

(i) Explain, using the laws of electromagnetic induction, how the device in the diagram acts as an electromagnetic brake.

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(3)

(ii) A conventional braking system has friction pads that are brought into contact with a moving metal surface when the vehicle is to be slowed down. State one advantage and one disadvantage of an electromagnetic brake compared to a conventional brake.

Advantage _____________________________________________________

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Disadvantage __________________________________________________

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(2)

(Total 8 marks)

Q2. A metal detector is moved horizontally at a constant speed just above the Earth’s surface to search for buried metal objects

Figure 1 shows the coil C of a metal detector moving over a circular bracelet made from a single band of metal. The planes of the coil and the bracelet are both horizontal.

Figure 1

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In this metal detector, C carries a direct current so that the magnetic flux produced by C does not vary. The bracelet is just below the surface, so the flux is perpendicular to the plane of the bracelet. The field is negligible outside the shaded region of C.

Figure 2 shows how the magnetic flux through the bracelet varies with time when C is moving at a constant velocity.

Figure 2

(a) (i) Sketch a graph on the grid to show how the emf induced in the bracelet varies with time as C moves across the bracelet. Use the same scale on the

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time axis as in Figure 2.

(3)

(ii) Use the laws of Faraday and Lenz to explain the shape of your graph.

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(4)

(b) The velocity at which C is moved is 0.28 m s−1.

Show that the diameter of the bracelet is about 6 cm.

(1)

(c) Determine the magnetic flux density of the field produced by C at the position of the bracelet.

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magnetic flux density ____________________ T

(2)

(d) Determine the maximum emf induced in the bracelet.

maximum emf ____________________ V

(3)

(Total 13 marks)

Q3. Figure 1 shows two magnets, supported on a yoke, placed on an electronic balance.

Figure 1

The magnets produce a uniform horizontal magnetic field in the region between them. A copper wire DE is connected in the circuit shown in Figure 1 and is clamped horizontally at right angles to the magnetic field.

Figure 2 shows a simplified plan view of the copper wire and magnets.

Figure 2

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When the apparatus is assembled with the switch open, the reading on the electronic balance is set to 0.000 g. This reading changes to a positive value when the switch is closed.

(a) Which of the following correctly describes the direction of the force acting on the wire DE due to the magnetic field when the switch is closed?

Tick (✔) the correct box.

towards the left magnet in Figure 2

towards the right magnet in Figure 2

vertically up

vertically down

(1)

(b) Label the poles of the magnets by putting N or S on each of the two dashed lines in Figure 2.

(1)

(c) Define the tesla.

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(1)

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(d) The magnets are 5.00 cm long. When the current in the wire is 3.43 A the reading on the electronic balance is 0.620 g.

Assume the field is uniform and is zero beyond the length of the magnets.

Calculate the magnetic flux density between the magnets.

magnetic flux density = ____________________ T

(2)

(Total 5 marks)

Q4. (a) Figure 1 shows two coils, P and Q, linked by an iron bar. Coil P is connected to a

battery through a variable resistor and a switch S. Coil Q is connected to a centre-zero ammeter.

Figure 1

(i) Initially the variable resistor is set to its minimum resistance and S is open. Describe and explain what is observed on the ammeter when S is closed.

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(3)

(ii) With S still closed, the resistance of the variable resistor is suddenly increased.

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Compare what is now observed on the ammeter with what was observed in part (i). Explain why this differs from what was observed in part (i).

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(2)

(b) Figure 2 shows a 40-turn coil of cross-sectional area 3.6 × 10–3 m2 with its plane set at right angles to a uniform magnetic field of flux density 0.42 T.

Figure 2

(i) Calculate the magnitude of the magnetic flux linkage for the coil. State an appropriate unit for your answer.

flux linkage ____________________ unit ___________

(2)

(ii) The coil is rotated through 90° in a time of 0.50 s. Determine the mean emf in the coil.

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mean emf ____________________ V

(2)

(Total 9 marks)

Q5. A cyclotron has two D-shaped regions where the magnetic flux density is constant. The D-shaped regions are separated by a small gap. An alternating electric field between the D-shaped regions accelerates charged particles. The magnetic field causes the charged particles to follow a circular path.

The diagram shows the path followed by a proton that starts from O.

(a) Explain why it is not possible for the magnetic field to alter the speed of a proton while it is in one of the D-shaped regions.

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(1)

(b) Derive an expression to show that the time taken by a proton to travel round one semi-circular path is independent of the radius of the path.

(3)

(c) The maximum radius of the path followed by the proton is 0.55 m and the magnetic flux density of the uniform field is 0.44 T.

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Ignore any relativistic effects.

Calculate the maximum speed of a proton when it leaves the cyclotron.

maximum speed = ____________________ m s–1

(2)

(Total 6 marks)

Q6. Figure 1 shows an arrangement for investigating electromagnetic induction.

Figure 1

When the switch is closed there is a current in the coil in circuit X. The current is in a

clockwise direction as viewed from position P.

Circuit Y is viewed from position P.

(a) Explain how Lenz’s law predicts the direction of the induced current when the switch is opened and again when it is closed.

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(4)

An ‘Earth inductor’ consists of a 500 turn coil. Figure 2 and Figure 3 shows it set up to measure the horizontal component of the Earth’s magnetic field. When the coil is rotated an induced emf is produced.

Figure 2 Figure 3

The mean diameter of the turns on the coil is 35 cm. Figure 4 shows the output

recorded for the variation of potential difference V with time t when the coil is rotated

at 1.5 revolutions per second.

Figure 4

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(b) Determine the flux density, BH, of the horizontal component of the Earth’s magnetic

field.

horizontal component of flux density = _____________T

(3)

(Total 7 marks)

Q7. Which one of the following statements is the main reason for operating power lines at high voltage?

A Transformers are never perfectly efficient.

B High voltages are required by many industrial users of electricity.

C Electrical generators produce alternating current.

D For a given amount of transmitted power, increasing the voltage decreases the current.

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(Total 1 mark)

Q8. A train is travelling at 20 m s–1 along a horizontal track through a uniform magnetic field of flux density 4.0 × 10–5 T acting vertically downwards.

What is the emf induced between the ends of an axle 1.5 m long?

A 3.0 × 10–6V B 5.3 × 10–4V C 1.2 × 10–3V D 7.5 × 105V

(Total 1 mark)

Q9. The diagram shows a horizontal conductor of length 50 mm carrying a current of 3.0 A at right angles to a uniform horizontal magnetic field of flux density 0.50 T.

What is the magnitude and direction of the magnetic force on the conductor ?

A 0.075 N vertically upwards B 0.075 N vertically downwards C 75 N vertically upwards D 75 N vertically downwards

(Total 1 mark)

Q10. The diagram shows a coil placed in a uniform magnetic field. In the position shown, the

angle between the normal to the plane of the coil and the magnetic field is is rad.

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Which line, A to D, in the table shows the angles through which the coil should be rotated, and the direction of rotation, so that the flux linkage becomes (i) a maximum, and (ii) a minimum?

Angle of rotation / rad

(i) for maximum flux linkage (ii) for minimum flux linkage

A clockwise anticlockwise

B anticlockwise clockwise

C clockwise anticlockwise

D anticlockwise clockwise

(Total 1 mark)

Q11. The primary coil of a step-up transformer is connected to a source of alternating pd. The secondary coil is connected to a lamp.

Which line, A to D, in the table correctly describes the ratios of flux linkages and currents through the secondary coil in relation to the primary coil?

Secondary magnetic flux linkage

Primary magnetic flux linkage

Secondary current

Primary current

A < 1 < 1

B > 1 < 1

C > 1 > 1

D < 1 > 1

(Total 1 mark)

Q12. A horizontal straight wire of length 0.30 m carries a current of 2.0 A perpendicular to a horizontal uniform magnetic field of flux density 5.0 × 10–2 T. The wire ‘floats’ in equilibrium in the field.

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What is the mass of the wire?

A 8.0 × 10–4 kg

B 3.1 × 10–3 kg

C 3.0 × 10–2 kg

D 8.2 × 10–1 kg

(Total 1 mark)

Q13.

Charged particles, each of mass m and charge Q, travel at a constant speed in a circle of

radius r in a uniform magnetic field of flux density B.

Which expression gives the frequency of rotation of a particle in the beam?

A

B

C

D

(Total 1 mark)

Q14.

A vertical conducting rod of length l is moved at a constant velocity v through a uniform

horizontal magnetic field of flux density B.

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Which of the rows gives a correct expression for the induced emf between the ends of the rod for the stated direction of the motion of the rod?

Direction of motion Induced

emf

A Vertical

B Horizontal at right angles to the field

Blv

C Vertical Blv

D Horizontal at right angles to the field

(Total 1 mark)

Q15.

The graph shows how the flux linkage, NΦ, through a coil changes when the coil is

moved into a magnetic field.

The emf induced in the coil

A decreases then becomes zero after time t0.

B increases then becomes constant after time

t0.

C is constant then becomes zero after time t0.

D is zero then increases after time t0.

(Total 1 mark)

Q16. A coil with 20 circular turns each of diameter 60 mm is placed in a uniform magnetic field of flux density 90 mT.

Initially the plane of the coil is perpendicular to the magnetic field lines as shown in Figure

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X.

The coil is rotated about a vertical axis by 90° in a time of 0.20 s so that its plane becomes parallel to the field lines as shown in Figure Y. Assume that the rate of change of flux linkage remains constant.

What is the emf induced in the coil?

A zero

B 1.3 mV

C 25 mV

D 100 mV

(Total 1 mark)

Q17. The diagram shows a rigidly-clamped straight horizontal current-carrying wire held mid-way between the poles of a magnet on a top-pan balance. The wire is perpendicular to the magnetic field direction.

The balance, which was zeroed before the switch was closed, read 161 g after the switch was closed. When the current is reversed and doubled, what would be the new reading on the balance?

A −322 g

B −161 g

C zero

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D 322 g

(Total 1 mark)

Q18. Four rectangular loops of wire A, B, C and D are each placed in a uniform magnetic field

of the same flux density B. The direction of the magnetic field is parallel to the plane of

the loops as shown.

When a current of 1 A is passed through each of the loops, magnetic forces act on them. The lengths of the sides of the loops are as shown. Which loop experiences the largest couple?

A B C D

(Total 1 mark)

Q19. Which one of the following statements is correct?

An electron follows a circular path when it is moving at right angles to

A a uniform magnetic field.

B a uniform electric field.

C uniform electric and magnetic fields which are perpendicular.

D uniform electric and magnetic fields which are in opposite directions.

(Total 1 mark)

Q20.

Two electrons, X and Y, travel at right angles to a uniform magnetic field.

X experiences a magnetic force, FX, and Y experiences a magnetic force, FY.

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What is the ratio if the kinetic energy of X is half that of Y?

A

B

C

D 1

(Total 1 mark)

Q21. A lamp rated at 12 V 60 W is connected to the secondary coil of a step-down transformer and is at full brightness. The primary coil is connected to a supply of 230 V. The transformer is 75% efficient. What is the current in the primary coil?

A 0.25 A

B 0.35 A

C 3.75 A

D 5.0 A

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Mark schemes

Q1. (a) (Faraday’s law)

(induced) emf ∞ rate of change of flux (linkage) ✔

(Lenz’s law)

direction of induced emf (or current) ✔

is such as to oppose the change (in flux) producing it ✔

In either order.

Allow “(induced) emf = rate of change of flux linkage”.

Ignore incorrect reference to names of laws. 3

(b) (i) current in coil produces magnetic field or flux

(that passes through disc) ✔

rotating disc cuts flux inducing / producing emf or current (in disc) ✔

induced (eddy) currents (in disc) interact with magnetic field ✔

force on (eddy) currents slows (or opposes) rotation (of disc) ✔

Alternative for last two points:

(eddy) currents in disc cause heating of disc ✔

energy for heating comes from ke of disc or vehicle (which is

slowed) ✔ max 3

(ii) Advantage: any one ✔

• no material (eg pads or discs or drums) to wear out • no pads needing replacement • no additional (or fewer) moving parts

Disadvantage: any one ✔

• ineffective at low speed or when stationary • dependent on vehicle’s electrical system remaining in working order • requires an electrical circuit (or source of electrical energy) to operate

whereas pads do not

Answers must refer to advantages and disadvantages of the electromagnetic brake.

Only accept points from these lists. 2

[8]

Q2. (a) (i) graph showing two pulses one at start and the other at the end with no emf

between the pulses

Positive and negative pulses shown

Similar shaped ‘curved’ pulses : negative between 0 and 0.22 ± 0.02 s and positive pulse 0.58 ± 0.02 and 0.8

3

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(ii) emf induced when the flux is changing or induced emf depends on the rate of change of flux

emf induced when flux changes between 0 and 0.2(2) s and / or between 0.6(0.58)s and 0.8 s OR no change in flux between 0.2 and 0.6 so no induced emf

Induced emf / current produces a field to oppose the change producing it.

Flux linking bracelet increases as the bracelet enters the field produced by C and decreases as it leaves so opposite emfs

4

(b) (Takes 0.21 s or 0.22 s for flux to change from 0 to maximum so) diameter = 0.28 × 0.21 = 0.059 (0.588) (m) or 0.28 × 0.22 = 0.062 (0.616) (m)

must be to at least 2sf 1

(c) Area of bracelet = 3.14 × 0.0312

B = 1120 × 10-6 / (3.14 × 0.0312) = 0.38 (T) B = 0.40 T if 3 cm used for radius

Condone incorrect power of 10

Allow answers in range 0.38T to 0.41 T (depends on value used for r)

2

(d) Use of steepest gradient of graph or tangent drawn on Figure 2 Correct data from tangent or points on the steepest part of the graph 10 to 11 mV

3

[13]

Q3.

(a) Vertically up (third row of table) ✔ 1

(b) (Using Flemings LHR) the configuration of the letters is S

N ✔

Answer must be near / on the dashed lines. 1

(c) The tesla is the (strength) of the magnetic field / flux density that produces a force of 1 newton in a wire of length 1m with

1 ampere (flowing perpendicular to the field). ✔

(owtte but must contain 1N, 1A and 1m)

For mark a reference to 1N, 1A and 1m must be seen. However the word ‘unit’ is equivalent to ‘1’.

E.g. unit force = 1N.

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Do not allow definitions based on F = Bqv. 1

(d) Use of (B = F / I l) = m g / I l ✔ (mark may come from

substitution as in next line)

Treat power of 10 error as an AE so lose one mark only.

B = 0.620 × 10–3 × 9.81 / (3.43 × 0.0500) = 0.035 or 0.036

(T) ✔

Lack of use of ‘g’ is a PE and scores zero. 2

[5]

Q4.

(a) (i) meter deflects then returns to zero ✓

current produces (magnetic) field / flux ✓

change in field / flux through Q induces emf ✓

induced emf causes current in Q (and meter) ✓

Deflection to right (condone left) then zero is equivalent to 1st mark.

Accept momentary deflection for 1st point.

“Change in field / flux induces current in Q” is just ✓ from the

last two marking points. max 3

(ii) meter deflects in opposite direction (or to left, or ecf) ✓

field / flux through P is reduced ✓

induces emf / current in opposite direction ✓

Ignore references to magnitude of deflection. max 2

(b) (i) flux linkage (= nΦ = nBA) = 40 × 0.42 × 3.6 × 10 −3

= 6.0(5) × 10−2 ✓

Unit mark is independent.

Allow 6 × 10−2.

Wb turns ✓

Accept 60 mWb turns if this unit is made clear.

Unit: allow Wb. 2

(ii) change in flux linkage = Δ(nΦ)= 6.05 × 10−2 (Wb turns) ✓

induced emf = = 0.12(1) (V) ✓

Essential to appreciate that 6.05 × 10−2 is change in flux linkage for 1st mark. Otherwise mark to max 1.

2

[9]

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Q5. (a) It is not possible as the force (due to the magnetic field) is

perpendicular to the motion / direction of travel / velocity ✔ (it

can only change the charged particle’s direction or alternatively no work is done on the proton) Or No component of force in the direction of motion.

The main part being examined is the reference to the force being perpendicular to the motion.

1

(b) B Q v = m v2 / r ✔

tsemi-circle (= distance / speed ) = π r / v

Or use of tcircle (= distance / speed ) = 2 π r / v ✔(this mark

can only be awarded if it follows an attempt to answer the first mark) combining gives

(tcircle = 2π m / B Q so)

tsemi-circle = π m / B Q

(which does not contain r / is independent of r) ✔

Accept ‘e’ if used instead of ‘Q’

Alternatives can be given for the first two marks.

1st needs a centripetal force term.

2nd is a circular motion expression to enable r to be removed.

3

(c) (rearranging first equation in (b) or from data booklet v = B Q r / m )

v = 0.44 × 1.6 × 10–19 × 0.55 / 1.67 × 10–27 ✔

v = 2.3 × 107 (m s–1) ✔

Correct answer scores both marks. 2

[6]

Q6.

(a) Induced current such as to opposes the change producing it✓

Switch on current increases the flux through Y✓

Current opposite direction / anticlockwise to create opposing flux✓

Switch off flux thorough Y due to X decreases so current travels clockwise to

create flux to oppose the decrease✓

one marks for Lenz’s law statement

two for explaining what happens at switch on OR switch off adequately

one for completing the argument for switch on and off adequately

4

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(b) Determines correctly in the calculation two of Vpk( 5.6±1 μV) , A (0.096 m2)

and ω(9.4 rad s-1)β✓

Substitutes all three in v = BAnω ignoring powers of 10 and calculation errors

for A and / or ω provided they have been attempted with working shown✓

BH = 12.4 nT✓

Allow 2 or 3 sf 3

[7]

Q7. D

[1]

Q8. C

[1]

Q9. A

[1]

Q10. D

[1]

Q11. B

[1]

Q12. B

[1]

Q13. A

[1]

Q14. B

[1]

Q15.

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C

[1]

Q16. C

[1]

Q17. A

[1]

Q18. B

[1]

Q19. A

[1]

Q20. C

[1]

Q21. B

[1]