1

Section AAnswer ALL questions.

1 An oil drop D carries a charge 4e, where e is the charge of electron. The drop is placedbetween two plates which are 5 mm apart and at a potential difference of 600 V. Calculate themass of the oil drop. [g = 10 m s-2]

5 mmD4e

+

-

600 V

A 7.7 x 10-15 kg B 5.2 x 10-15 kg C 3.0 x 10-14 kg D 1.2 x 10-15 kg

2 The diagram below shows three point charg es +q1, –q2 and +q3 of equal magnitude1.29 x 10-6 C lying on a straight line.

What is the resultant force exerted on the point charge q3 by the other two point charges?A 28 N B 2.8 x 10-5 N C -2.8 x 10-5 N D -28 N

3 To increase the capacitance of a parallel plate capacitor, which of the following quantitymust be increased ?

A Surface area of the plates.B The distance of separation of the plates.C The voltage applied across the plates.D The thickness of the plates.

4. When the potential difference across a metallic conductor is increased, which of thefollowing statements is true?

A The electric field intensity in the conductor remains the same.B The drift velocity of the charge carriers increases.C The charge carrier per unit volume increases.D The current density remains the same.

5. An electron moves into a uniform magnetic field with a certain velocity. If the velocity ofthe electron is in the same direction as the magnetic field, which of the following statementsabout the subsequent motion of the electron in the magnetic field is true ?. A The electron accelerates to the le ft. B The electron accelerates to the right. C The electron continues to move with its original velocity. D The electron is deflected and moves in a circle at constant speed

-q2+q1

2.0cm

4.0 cm

+q3

2

6. The planes of vibration of the electric and magnetic fields in an electromagnetic wave are

A parallel to each other and parallel to the direction of the propagation of the waveB parallel to each other and perpendicular to the direction of the pro pagation of the waveC perpendicular to each other and parallel to the direction of the propagation of thewaveD perpendicular to each other and perpendicular to the direction of the propagation ofthe wave

7.

What is the total force exerted on the point charge q3 by the other two point charges?A 28 N B 2.8 x 10-5 N C -2.8 x 10-5 N D -28 N

8. Diagram below shows three capacitors connected between XY. A 12.0 V battery is appliedacross XY.

The potential difference across the 4 μF capacitor isA 6.67 V B 2.2 V C 22 V D 26.7 V

9. Two capacitors with capacitance C and 3C, are charged to a potential difference of V and2 V respectively. If the positively charged plates of the capacitors are connected and thenegatively charged plates are connected too, the system of capacitors will experience

A an increase in charge but a loss in energyB an increase in energy but a loss in chargeC a loss in both energy and chargeD a loss in energy but the charge remains constant

X4μF

2μF

Y

3μF

-q2+q1

2.0cm

4.0 cm

+q3

3

X

Y

4

4

4

5 5

6 V

10. The diagram below shows a Wheatstone bridge. S is known to be 30 Ω. The circuit isbalanced when a resistance of 150 Ω is connected directly across S. The positions of P and Qare exchanged and the resistance of 150 Ω across S is removed. The circuit is balanced againwhen a resistance of 380 Ω is connected directly across S.

The ratio of P : Q is

A 0.2 B 0.39 C 0.95 D 1.05

11. A moving coil meter of resistance 100 Ω indicates full -scale deflection when a current of100 μA flows through it. If the meter is required to indicate full -scale deflection when a currentof 1 mA flows in the circuit, the resistance of the shunt to be connected across the meter has tobe

A 9 Ω B 10 Ω C9

100 Ω D 900 Ω

12 The diagram below shows an electric circuit.

The potential difference between the points X and Y isA 1.0 V B 2.0 V C 3.0 V D 6.0 V

P Q

R S

G

4

13. A galvanometer which has a resistance of 2 Ω gives a full scale-deflection when acurrent of 1 mA flows through it. The galvanometer is being modified to measure currents upto several amperes. Which of the following modified arrangements is correct?

G

5 m

G

5 k

A B

G G5 k 5 m

C D

14. A beam of electrons moves in a straight path through a region which ha s uniform electricand magnetic fields. The electric field is produced by two parallel metal plates which are 4.0 cmapart with a potential difference of 1000 V. If the speed of the electrons is 2.5 x 10 6 m s-1, themagnetic flux density is

A 1.0 x 10-1 T B 1.0 x 10-2 T C 1.0 x 10-3 T D 1.0 x 10-4 T

15. Which of the following factors does not affect the magnetic flux density of the magneticfield at the centre of a plane circular coil ?

A The number of turns of the coil.B The magnitude of the current flowing in the coil.C The diameter of the coil.D The thickness of the wire of the coil.

5

Section B ( 15 marks )Answer ALL questions in this section.

16 (a) Define electric field strength, E and electric potential, V at a point in an electric field.

[ 2 marks ](b) Two equal positive point charges Q 1 and Q2 of charge q are fixed along x-axis at positionx = –a and x = +a as shown in the diagram below.

(i) What is the resultant electric field, E at the origin O.

[ 1 mark ]

(ii) What is the resultant electric potential, V at the origin O in terms of q and a?

[ 2 marks]A third identical charge Q 3 is fixed at a distance 2a from Q1 and Q2 as shown in the diagram below.

(iii) What is the resultant electric field strength, E and the resultant V at O?

[3 marks]

O

Q1 Q2

+a-a

OQ1 Q2

+a-a

Q3

6

17 (a) The figure below shows a proton moves with velocity v and enters perpendicularlyinto a uniform magnetic field B . It moves in a circular path of radius, r.

(i) Sketch the path in the diagram above showing the direction of the motion of the proton.[1 mark]

(ii) In the figure above, draw the direction of electric field E required so that the proton continues tomove without deflection. [ 1 mark]

(iii) Derive an expression for the magnitude of the electric field strength E required for thecondition stated in a(ii) .

[2 marks](iv) A deuterium ion with velocity v which is equal to the velocity of proton in (a) , enters thesame arrangement of B and E. Explain the subsequent path of the deuterium ion.………………………………………………………………………………………………….………………………………………………………………………………………………[1 mark]

(v) If the mass of the proton is m, shows that the frequency, f of the circular motion of the proton isindependent of its velocity,v

[ 2 marks ]

7

20 40 60 80 100 t(s)

10V/V

8

6

4

2

0

Section C ( 30 marks )Answer any two questions in this section.

18 (a) Define time constant, τ for a capacitor. [ 1mark ]A circuit containing a capacitor, C and a resistor, R of value 10 M Ω are connected as shown in thediagram below.

The switch is closed to A and after capacitor C is fully charged, the separation of the plates isslightly reduced. State the effect of this change on(i) the capacitance. [1mark](ii) the potential difference across the plates. [1mark](iii) the charges stored in the capacitor. [1mark ]

(b) Switch S is then closed to B. The figure below shows a graph of voltage V across the capacitoragainst time t.

Based on the graph(i) What is the e.m.f ,E of the battery? [1 mark ](ii) Calculate the ratio of V to E when t = τ. [3 marks](iii) Calculate the value V at time t = τ and determine the value τ from the graph. [3 marks](iv) Calculate the capacitance of the capacitor. [2 marks](v) Calculate the total energy stored in the capacitor. [2marks]

A

B C RS

E

8

19 (a) State Kirchhoff’s laws. Explain how each is based on a fundamental physical principle.[4 marks]

(b) Use the laws to deduce values of the currents I a, Ib, Ic and Id as shown in thecircuits below.

[ 8 marks]

(c) Two resistors having resistances of 1.8 kΩ and 4.7 kΩ are connected in series with a battery ofe.m.f. 12 V and negligible internal resistance as shown in the diagram below.

Calculate the potential diffe rence across each of the resistors . [3 marks]

2V

2Ω

2V

2Ω

3Ω

IC Id

2V

3Ω

1V

3Ω

Ia

Ib

4Ω

9

20 (a) A magnetic field B passing through a horizontal wire loop PQRS of an area A and making an angle θ with the plane of the loop is shown in the diagram below.

(i) Express, in terms of B, A, and θ, the magneti cflux Ф through the loop. [1 mark]

(ii) State two alterations which can produce induced e.m.f in the loop. [2 marks]

(iii) If the magnetic flux through the plane of the loop PQRS is reduced, what is the direction of the induced current in the loop? State the law used. [2 marks]

(b) (i) Define self-inductance. [2marks]

(ii) An inductor in the form of a solenoid haslength l, cross-sectional area A and total turns N. Show that the self-inductance L is given by

lANL

20

where μ0 is the permeability of free space. [2 marks]

(c) A 50.0 Hz a.c generator consists of a coil of N turns and area 2.0 x 10 -2 m2 which rotates in a uniform magnetic field of 0.15T. Calculate N so that the root mean square voltage produced is 240 V. [3 marks]

(d) (i) At the moment an electric motor is switched on, a large amount of current flows in the armature and causes damage. Why does this happen? [1mark]

(ii) The electric motor is usually connected to an inductor to avoid the above situation from occuring. How can the inductor help avoid the damage? [2 marks]

END OF QUESTION PAPER

1

MARK SCHEME – PHYSICS STPM TRIAL PAPER 2UPPER 6 STPM (NEW) 2013

Section A

1 A 11 C2 D 12 A3 A 13 B4 B 14 B5 C 15 D6 D7 D8 A9 D10 D

Section B

answer16 (a) Electric field strength, E is force per unit positive charge at that point....... 1 markElectric potential is the work done to bring a unit positive charge from infinity to the point. ..1 m

(b) (i) zero ... 1mark(ii)

aq

aq

aqV

0

00

42

44

OR

aq1010801 .

(iii) Distance Q3 to O = 332 222 aaaa )(

)( 20 34 aq

qFER

2012 a

q

OR 291003

aq

. acting downward

...... 1mark

....... 1 mark

...... 1mark

....... 1 mark

2

aq

aq

aq

aq

aqV

10

0

000

10322

3111

4

3444

.

17 (a) i) Deflection and direction ( Anticlockwise circular or curve motion ) 1 markii) Direction of E 1 mark

iii) Magnetic force = electric forceBev = eE .... 1mE = Bv .... 1m

(iv) a straight line , v depends on E and B , not on mass (deuterium has higher mass) 1 mark

BEv

17(v) Frequency,2

f

qvB = mrω2 v = rω ........................................ 1 markq(rω)B = m(rω) ωqB = mω => qB =m(2πf)

mqBf2

............................................ 1 mark

independent of v

..... 1m

3

18 (a) time taken for the charge stored in the capacitor plates to decrease toe1 of its initial

value. ...1mark

(i) C increases .......1mark

(dAC 0 ε0 and A are constant

C αd1 ; d is decreased, )

(ii) Potential difference remains consta nt; same battery is used. ....1 mark

(iii)VQC , V is constant ;C increased, Q increased ..... 1mark

18 (b) (i) E = 9.0 V ...1 mark

(ii)

CRt

eEV 1 ...1mark

When t = τ = CR11 e

EV ........ 1mark

=0.63 .....1 mark

(iii) V = 0.63 E ....... 1mark= 0.63 x 9.0= 5.7 V .... 1 mark

From graph t = 10s (answer between 9 -11s) .....1mark

(iv)R

C ........1mark

F6

6

100.11010

10

Answer between 0.9 x 10 -6 to 1.1 x 10-6 F

(v) Energy = 2

21 CVU .........1mark

26 75100121 ).)(.( U =

=1.62 x 10-5 J ......1mark

.....1mark

4

19

20 (a) (i) Magnetic flux, Ф = (B sin θ )A .....1m (ii) 1. Rotate the coil about an axis parallel to the plane of the coil.

2. Remove the coil from the magnetic field. 3. Reduce or increase the magnetic flux density, B.

(Any two – 1 mark each)

(iii ) PQRSP or PQ QR RS SP .... 1 mark

Lenz’s law ..... 1m(states that the direction of the induced current is such as to oppose the change in the magneticflux linked with the coil.)(When the magnetic field is reduced, the induced current flows in the direction PQRSP so thatthe magnetic field in the coil produced by the current is in the original direction of B.)

(b) (i) FromdtdILE

dtdIEL

inductortheincurrentofchangeofrateinductortheininducede.m.f.

....... 2 or 0 marks

OR the ratio of the electromotive force produced in a circuit by self -induction to the rate ofchange of current producing it.

(ii) Magnetic flux, Ф = LI = NBA, and IlNB

0

.... 1m

IAlNNLI

0 ...... 1m

5

lANL

20

(c) Maximum e.m.f induced, E0 = NBAω ... 1m

r.m.s. voltage produced, Vr.m.s 2402

NBA ... 1m

)().(. 5021002150

24022

N

= 360 turns ... 1m

(d) (i) No back e.m.f is induced yet. ... 1m

OR Current in armature,

RVI0 V = applied voltage, R = resistance of the coil

R small, current I is large, causes the coil to be heated up.

(ii) When the motor is switched on, the change of current in the inductor produces a back e.m.f... 1m

that reduces the current. ... 1m