Solutions for electromagnetism

Electromagnetism

1. ACJC_08H2P1_Q30 In a particle collision experiment, electrons with a kinetic energy of 250 eV are required. In order to obtain an electron beam with this specific kinetic energy, accelerated electrons are passed through a velocity selector as shown below with plate Y at a higher potential compared to plate X.

Which of the following gives the correct effect of electrons in the “mixed energy’ electron beam that enters the velocity selector with kinetic energies that differs from the required 250 eV?

Electrons with Kinetic Energies Greater than 250 Ev

Electrons with Kinetic Energies Lower than 250 eV

A Impact on plate X Impact on plate X B Impact on plate X Impact on plate Y C Impact on plate Y Impact on plate X D Impact on plate Y Impact on plate Y

--------------------------------------------------------------------------------------------------------------------- 2. AJC_Physics Prelim_H2P1_Q30 A plotting compass is placed next to a vertical wire PQ. When there is no current in the wire, the compass on the horizontal plane ABCD points North as shown in the diagram. Which diagram shows a possible direction for the compass to point when a current passes from Q to P?

ANS: (D)

3. CJC_2008 Physics Prelim_H2P1_Q28 A small plastic sphere carrying a negative charge is maintained at a constant height by the action of a downward vertical electric field. A uniform magnetic field is applied in the same direction as the electric field. What does the sphere do?

A Move downwards in a spiral path

B Move in a horizontal circle

C Move upwards in a spiral path

D Remain stationary

Reason: Since the plastic sphere is stationary, the magnetic field will not have any effect on the plastic sphere. --------------------------------------------------------------------------------------------------------------------- 4. CJC_2008 Physics Prelim_H2P1_Q30 A charge particle is projected at right angles into a magnetic field as shown. Which of the following is correct?

A The momentum of the particle is increasing steadily

B The magnetic flux density is decreasing steadily

C The speed of the particle is decreasing steadily

D The charge of the particle is decreasing steadily

Reason:

Since radius decreases, the speed of the particle is decreasing steadily. ---------------------------------------------------------------------------------------------------------------------

5. IJC_2008 Physics Prelim_H2P1_Q28 A long, horizontal, straight wire is placed parallel to the plane of a coil as shown in the diagram. Both the coil and the wire carry currents in the directions indicated.

What is the direction of the force at point P on the wire due to these currents? A in the direction of X B in the direction of Y C out of the plane of the paper D into the plane of the paper Reason: Direction of magnetic field due to the coil is into the paper. Using Left Hand Rule, direction of force on wire at P is upwards --------------------------------------------------------------------------------------------------------------------- 6. IJC_2008 Physics Prelim_H2P1_Q29 X, Y and Z are three long parallel wires carrying currents in a vertical plane as shown.

The resultant force on wire Y is A zero B towards X C towards Z D perpendicular to the paper

Reason:

The force on Y due to Z is to the left. The force on Y due to X is also to the left. Hence the resultant force is to the left (towards X) --------------------------------------------------------------------------------------------------------------------- 7. JJC_2008 Physics Prelim_H2P1_Q28 A doubly charged ion is moving in a uniform magnetic field of flux density B in a circle of radius r at a speed v. What is the flux density which would maintain a singly-charged ion of the same mass in a circle of half the radius at the same speed?

A 4B

B 2B

C 2B

D 4B

Reason:

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8. JJC_2008 Physics Prelim_H2P1_Q29 The length of WX, XY and YZ are 10 cm each. Find the net force on the segment of wire, WXYZ, in the figure below if the strength of the magnetic field, B = 0.4 T and the current flowing through the wire is 5 A.

A 0.1 N into the plane of the page

B 0.1 N out of the plane of the page

C 0.2 N into the plane of the page

D 0.2 N out of the plane of the page

Reason:

--------------------------------------------------------------------------------------------------------------------- 9. PJC_2008 Physics Prelim_H2P1_Q26 The figure below shows three arrangements of circular loops, centered on vertical axes and carrying identical currents in the directions indicated. Rank the arrangement according to the magnitudes of the magnetic fields (from the smallest to the largest) at the midpoints between the loops on the axes.

A 1, 2, 3

B 2, 1, 3

C 2, 3, 1

D 3, 1, 2

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10. PJC_2008 Physics Prelim_H2P1_Q27 A wire of length 5.0 cm is placed at right angles to a magnetic field of flux density 0.040 T. The wire makes an angle θ with the line PQ and carries a current of 6.0 A.

As the angle θ increases from 0 to 360 , which of the following is true about the

magnitude of the force which the field exerts on the wire? A The force varies between 0 N to 0.012 N.

B The force varies between 0.012 N to 0.12 N.

C The force is constant at 0 N.

D The force is constant at 0.012 N.

Reason:

--------------------------------------------------------------------------------------------------------------------- 11. RJC_2008 Physics Prelim_H2P1_Q29

The figure below shows a square coil WXYZ of sides 0.25 m, lying in a vertical plane and carrying a current I of 2.0 A. The magnetic flux density B of 0.010 T is parallel to XY.

What is the magnitude of the torque and its direction when viewed from the top?

A 31.3 10 N m, anticlockwise

B 31.3 10 N m, clockwise

C 32.5 10 N m, anticlockwise

D 32.5 10 N m, clockwise

--------------------------------------------------------------------------------------------------------------------- 12. RJC_2008 Physics Prelim_H2P1_Q30 The diagram below shows three parallel wires X, Y and Z placed in a horizontal plane. Wires X and Z carry current I in opposite directions. Wire Y carries a current of 3I in the direction shown and is equidistant from the other wires.

If the magnitude of the force per unit length acting between two parallel wires placed a distance d apart, each carrying a current of I, is 2.0 × 10-6 N m-1, what is the direction and magnitude of the net force per unit length acting on wire Z?

[The force per unit length is proportional to the product of the currents in the two wires and inversely proportional to the separation between them.]

Direction Magnitude

A Towards Y 6 -12.0 10 N m

B Towards Y 6 -15.0 10 N m

C Away from Y 6 -15.0 10 N m

D Away from Y 6 -17.0 10 N m

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13. SAJC_2008 Physics Prelim_H2P1_Q25 Two long insulated wires, X and Y, are placed perpendicularly to each other, one on top of the other as shown in the figure below. Each wire carries the same current in the direction shown.

What is the direction of the force acting on wire Y at point Z, due to the current in X? A Out of the page B Into the page C Upwards D Downwards --------------------------------------------------------------------------------------------------------------------- 14. YJC_2008 Physics Prelim_H2P1_Q27 Three long, parallel conductors, Q, R and S carry currents of equal magnitude. The figure below shows the plan view of the conductors, whereby the current in S is opposite in direction to those in Q and R.

Given that the magnetic field strength at a point of distance r from a conductor that carries a current I is

2

oIBr

and the distance between Q and R is 2a, determine the direction of the resultant magnetic field at point P.

ANS: (B) --------------------------------------------------------------------------------------------------------------------- 15. YJC_2008 Physics Prelim_H2P1_Q30 A heating element is placed a distance s from a flat electron detector. A uniform magnetic field of flux density B is applied in the direction shown in the fgure below.

Electrons of mass m and charge q are emitted from the heating filament towards the detector. Determine the minimum speed of thermionic electrons hat are registered by the detector.

A 2Bq

m C

Bqs

m

B

1

22Bq

m

D

1

2Bqs

m

------------------------------------------------------------------------------------------------------------ 16. SRJC_2008 Physics Prelim_H2P1_Q24 A beam of electrons is directed into a region of uniform electric field as shown in the figure below.

Which of the following statements best describes the path of the beam of electrons within the field? A Beam of electrons deflects out of page. B Beam of electrons deflects into page. C Beam of electrons deflects downwards. D Beam of electrons deflects upwards. ------------------------------------------------------------------------------------------------------------ 17. SRJC_2008 Physics Prelim_H2P1_Q29 Three current-carrying conductors X, Y and Z are placed perpendicular to the plane of the page as shown in figure below.

In which of the following directions does the resultant force on Z act?

ANS: (B) ---------------------------------------------------------------------------------------------------------------------

18. SRJC_2008 Physics Prelim_H2P1_Q30 Which of the following pair define the magnetic flux density and the tesla? Magnetic flux density Tesla

A The number of magnetic flux lines per unit area where a current-carrying conductor is placed.

The magnetic flux density of a wire of length one metre carrying a current of one ampere has a force of one newton in a direction at right angles to both the flux and the current.

B The force per unit current per unit length of the conductor when the conductor is at right angles to the field.

The force acting on a wire of length one metre and carrying a current of one ampere when it is placed at right angles to the magnetic field.

C The number of magnetic flux lines per unit area where a current-carrying conductor is placed.

The force acting on a wire of length one metre and carrying a current of one ampere when it is placed at right angles to the magnetic field.

D The force per unit current per unit length of the conductor when the conductor is at right angles to the field.

The magnetic flux density of a wire of length one metre carrying a current of one ampere has a force of one newton in a direction at right angles to both the flux and the current.

--------------------------------------------------------------------------------------------------------------------- 19. MJC_2008 Physics Prelim_H2P1_Q29 The figure below shows the top view of a current carrying coil in a uniform magnetic field at a particular instant in time. The current at P is flowing perpendicularly into the plane of the paper and the current at Q is flowing perpendicularly out of the plane of the paper.

Which of the following correctly shows the direction of the forces, F acting on the coil at that instant in time?

ANS: A Reason: Use Left Hand Rule, direction of force is perpendicular to current and B-field. --------------------------------------------------------------------------------------------------------------------- 20. MJC_2008 Physics Prelim_H2P1_Q30 Two parallel conductors carry sinusoidal alternating currents that differ in phase by π radian. The diagram shows the flow of current at one particular instance in time.

Which of the following graphs shows a possible variation of the force, with respect to time, experienced by one of the conductors?

ANS: (C) Reasoning: Currents in opposite dir repel. Since current is sinusoidal, the force should also varies sinusoidally. Since it consistently repels, the force should always be positive or negative (depending on the sign convention used). Option A suggests that sometimes it repels, sometimes attracts, due to a change in signs for F. --------------------------------------------------------------------------------------------------------------------- 21. DHS_2008 Physics Prelim_H2P1_Q29 Jamie placed three long straight wires P, Q and R normal to the plane of paper as shown in the diagram below. Wires P and Q carry currents directed into the paper, and wire R carries a current directed out of the paper. All three current have the same magnitude.

Which arrow best shows the direction of the resultant force on wire R? ANS: (A)

--------------------------------------------------------------------------------------------------------------------- 22. DHS_2008 Physics Prelim_H2P1_Q29 In an experiment to study the path of a charged particle in a uniform magnetic field, Yunshan observed that one particle travelled in the path as shown below.

Which of the following is not a possible cause for the path? A The magnetic field density is increasing B The charge on the particle is increasing C The momentum of the particle is increasing D The mass/charge ratio of the particle is decreasing Reasoning: Assuming the B field is normal to the page.

2

2

mvqvB

R

mv mvR

qvB qB

Since R is decreasing, mv cannot be increasing.

--------------------------------------------------------------------------------------------------------------------- 23. NJC_2008 Physics Prelim_H2P1_Q24 A beam of charged particles enters a region of electric field produced by 2 charged parallel plates and then deflected as shown in the diagram below.

Which of the following changes would reduce the deflection? A Reduce the initial velocity of the electrons. B Reduce the separation between the plates. C Reduce the potential differences between the plates. D Reduce the mass of the charged particles. --------------------------------------------------------------------------------------------------------------------- 24. NJC_2008 Physics Prelim_H2P1_Q30 In the diagram below, P is a horizontal circular coil of wire carrying a current I1. QR is a conducting rod placed on the same plane, supported by 2 horizontal parallel rails which are perpendicular to QR and carry a current I2 as shown.

The rod QR will experience A a magnetic force along the direction QS. B a magnetic force along the direction TR. C a magnetic force perpendicularly upwards from the plane of the coil. D no magnetic force at all. --------------------------------------------------------------------------------------------------------------------- 25. VJC_2008 Physics Prelim_H2P1_Q23 An electron passes between two oppositely charged metal plates, which are separated by 15 cm and have a potential difference of 20V between them.

The electron takes 71.0 10 s to pass through the region between the plates. What is the

vertical deflection, d of the electron after emerging from the region.

A 0.12 cm B 1.8 cm C 12 cm D 23 cm --------------------------------------------------------------------------------------------------------------------- 26. VJC_2008 Physics Prelim_H2P1_Q28 A straight conductor PQ of length 0.50 m is place in a magnetic field of flux density 0.15 T parallel to the plane of the diagram.

What is the magnetic force on the conductor PQ if it carries a current of 5.0 A?

A 0.23 N

B 0.28 N

C 0.30 N

D 0.38 N

27. ACJC_08H2P2_Q3

(a) Define magnetic flux density and the tesla.

___________________________________________________________________

_________________________________________________________________[2]

(b) Sketch the magnetic flux patterns due to the following:

[3]

(c) A galvanometer has a square coil of sides 2.0 cm and consists of 40 turns of wire.

The coil is placed in two curved-poled magnets as shown below of flux density 0.60

T so that for whatever positions of the coil, the magnetic field is always parallel to the

plane of the coil. The coil with an attached pointer is held centrally between the

curved-pole magnets. The coil moves in the annular space between the soft-iron

core and the magnet. A restraining torque, provided by the spiral springs placed

above and below the coil is used to measure the current I flowing through the coil.

(i) a long straight current carrying wire

(ii) a flat circular current carrying coil

(i) When a current of 2.0 mA passes through the windings of the coil, determine the

torque on the coil due to the magnetic force.

Torque = ________ Nm [3]

(ii) Suggest a reason why it is necessary for a radial field to be used to ensure that

the magnetic field is always parallel to the plane of the coil.

________________________________________________________________

______________________________________________________________[1]

Solution

(a)

Magnetic flux density is the force acting per unit length per unit current on a

conductor placed at right angles to this external magnetic field.

One tesla is the magnetic flux density of a magnetic field when a conductor of length

1 metre carrying a current of 1 ampere placed perpendicular to this field experiences

a force of 1 newton in a direction which is perpendicular to both the field and the

current.

(b) i.

Correct shape(draw using compasses, and with increasing separation)

(b) ii.

Correct shape (shows stronger field on inside, almost uniform)

Direction for both correct

(c) i

3 0

5

Torque on coil due to magnetic force

sin

40 0.60 2.0 10 0.02 sin 90 0.02

1.92 10 Nm

F d

NBIL d

(c) ii

By having the magnetic field always parallel to the plane of the coil, the torque on the

coil would then be only dependent on the current in the coil. This ensures that the angle

of deflection of the pointer would be proportional to current.

--------------------------------------------------------------------------------------------------------------------- 28. ACJC_08H2P2_Q7 (Part)

One possible explanation of the presence of magnetic field on Earth is the magnetic

dynamo theory. It says that the magnetic field is produced by swirling motions of liquid

conducting material in the planet interiors. Such materials are called metallic and are not

necessarily shiny solids like copper, aluminum, or iron. Jupiter and Saturn have a large

amount of hydrogen that is compressed so much it forms a liquid. Some of that liquid

hydrogen is in a state where some of the electrons are squeezed out of the atoms and

are free to move around.

A moving charge will produce a magnetic field. The liquid conducting material in a

planet's interior can be made to swirl about if the planet is rotating quickly enough.

Earth has a strong magnetic field because it spins fast (once every 23.93 hours), it has a

liquid conducting core made of liquid iron-nickel.

Mars is about half the diameter of the Earth and has about 1/10th the Earth's mass.

Mars spins quickly (once every 24.6 hours). Its metallic core is solid.

(a) Suggest with reasons whether Mars has a stronger or weaker magnetic field

compared to Earth.

___________________________________________________________________

_________________________________________________________________ [2]

(b) A planet's magnetic field forms a shield protecting the planet's surface from

energetic, charged particles coming from the Sun and other places. The Sun is

constantly sending out charged particles, mostly electrons, called the solar wind, into

the solar system. The particles have energy about 1 to 100 keV. When solar wind

particles run into a magnetic field, they are deflected and spiral around the magnetic

field lines.

An effect seen when the solar wind interacts with a planet's magnetic field is aurorae.

Aurorae are shimmering light displays produced by solar wind particles deflected

toward the magnetic poles and colliding with the molecules in the upper atmosphere.

These collisions excite the atmosphere molecules. The glow of the aurorae is due to

the emission line spectra of the atmosphere molecules.

(iii) By considering the Earth's magnetic field, suggest with reasons why Aurorae are

mostly seen in the polar region rather than the equatorial region.

________________________________________________________________

______________________________________________________________ [2]

Solution:

(a)

Even though Mars rotation is about the same as the Earth, the charges in the

metallic core in Mars may not spin as fast as liquid core’s charges in the Earth.

Therefore, Mars has weaker magnetic field.

(b) iii.

The direction of the entry of the solar wind (/electrons/ charged particles) and the

Earth’s magnetic field are almost perpendicular at the Equator, hence deflected away

from the Earth.

Direction of solar wind almost parallel to field lines at poles. Hence not deflected.

Thus Aurora sightings at the Equators are rare but not at the poles.

--------------------------------------------------------------------------------------------------------------------- 29. ACJC_08H2P3_Q3

(a) Define magnetic flux and explain what you understand by it.

___________________________________________________________________

_________________________________________________________________[2]

(b) The diagram below shows a wire PQ of length l and a vertical conducting frame of

negligible resistance placed in a uniform magnetic field B which is perpendicular to

the plane of the frame. A light bulb of resistance R is connected to the conducting

frame. The wire falls vertically from rest and slides in contact with the sides of the

conducting frame which has negligible friction.

(i) State and explain the direction of the induced current in wire PQ.

________________________________________________________________

______________________________________________________________[2]

(ii) Show that current I flowing through the light bulb is given by the expression

BlvI

R

[2]

(iii) Hence, determine the expression for the magnetic force acting on wire PQ in

terms of B, l, R and the velocity v of the wire PQ.

Expression = __________ [1]

(iv) Given that the mass of rod PQ is 5.0 g, l = 60 cm, B = 0.50 T and R = 8.0 Ω,

determine the terminal velocity of the rod.

Terminal Velocity = _________ m s-1 [3]

Solution:

(a)

The magnetic flux passing through any surface area is defined as the product of the

component of the magnetic flux density, B normal to the plane of the surface and

area of the surface A.

The larger the value of φ, the greater will be the number of magnetic field lines

passing through a given cross-sectional area.

(b) i

When PQ moves downwards, magnetic flux linkage through the conducting loop

increases. By Lenz’s law, the induced current must flow in clockwise manner in the

conducting loop so as to produce an induced magnetic field that is out of the plane of

the paper to reduce this increase in flux linkage.

Hence the induced current flows from P to Q.

(b) ii.

know than

Since

Blv

VI

R

Blv

R

(b) iii.

2 2

Force on a current carrying conductor

F BIL

B l v

R

(b) iv.

2 2

2 2

2 2

1

Force on a current carrying conductor

0.05 9.81 8

0.5 0.60

4.36 m s

B l vmg

R

mgRv

B l

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YJC_08H2P2_Q1

Fig. 1.1 shows electrons emitted from a heated cathode and accelerated from rest by a

potential difference between anode and cathode, towards the y-plates. The y-plates

are 2.0 cm long and placed 0.50 cm apart. When there is no electric field between

the y-plates, the beam will pass through undeflected. Ignore gravity effects.

(a) Given that the velocity of the electrons that enter the y-plates is

7 -11.80 10 m s , calculate the electric potential of the anode.

Potential of anode = ………………………… V [2]

(b) Given that the acceleration of the electrons within the y-plates is

15 21.76 10 m s , what is the value of the electric potential VP?

Potential VP = ………………………… V [2]

(c) Find the vertical displacement of the electrons when they just exit

from y-plates.

Vertical displacement = ………………………… m [2]

(d) In Fig. 1.1, sketch the path of electron beam when it is within the

region of the y-plates. [1]

(e) Describe and explain what happens to the vertical displacement when the

potential of the anode is increased. [2]

Solutions:

2

219 31 7

31 15

15

15

At terminal velocity,

weight of PQ Magnetic force on PQ

(a)

1

2

11.6 10 9.11 10 1.80 10

2

922 V

Anode's potential 922 100 822 V

(b)

9.11 10 1.76 10

1.6 10 N

1.6 10

1.6 10

e

e

qV mv

V

V

F ma

F qE

19

9

7

2

215 9

0

0.005

50 V

(c)

0.02horizontal motion: 1.11 10 s

1.80 10

vertical motion:

1

2

11.76 10 1.11 10

2

0.11 cm

p

p

V

V

t

s ut at

(d) Upward parabolic path

(e) When potential at anode is increased, velocity of electrons increased and hence the

time spent inside y-plates decreased. Therefore vertical displacement is decreased.

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