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1. The diagram shows the electric field lines produced by an electrostatic focussing device.
Which one of the following diagrams best shows the corresponding equipotential lines? Theelectric field lines are shown as broken lines on each of the diagrams.
A. B.
C. D.
(1)
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2. The diagram below shows lines of electric equipotential. The change in potential on movingfrom one line to the next is always the same. At which point does the electric field strengthhave its greatest magnitude?
A
B
C
D
(1)
3. The diagram below shows two lines of equipotential in a region of a uniform electric field. LineX has a potential of +50 V and line Y has a potential of +100V. The distance between X and Yis 2.0 cm.
+50 V +100 V
X Y
2.0 cm
2
Which one of the following correctly gives the direction of the electric field and its strength?
Direction Strength / V cm–1
A. X Y 25
B. X Y 100
C. Y X 25
D. Y X 100
(1)
4. The diagram below shows two parallel conducting plates that are oppositely charged.
+++ + +
– – –––
X
Y
The line XY is perpendicular to the plates.
3
Which of the following diagrams shows the variation along the line XY of the magnitude E ofthe electric field strength between the plates?
E
E
E
E
X
X
X
X
Y
Y
Y
Y
distance
distance
distance
distance
A. B.
C. D.
(1)
5. The electron volt is defined as
A. a unit of energy exactly equal to 1.6 × 10–19 J.
B. a fraction
of the ionization energy of atomic hydrogen.6.13
1
C. the energy gained by an electron when it moves through a potential difference of 1.0 V.
D. the energy transfer when 1.0 C of charge moves through a potential difference of 1.0 V.(1)
4
6. The diagram below shows electric field lines in a region of space.
X P Y
Which of the following diagrams best shows the variation with distance d of the potential Valong the line XY?
A.
C.
B.
D.
V
V
V
V
d
d
d
d
X
X
X
X
P
P
P
P
Y
Y
Y
Y(1)
5
7. A proton and an alpha particle are accelerated from rest from the positively charged plate X tothe negatively charged plate Y.
+
– – – – – –
+ + + + +
proton alpha particle
mid-point
Y
X
At the mid-point between the plates, the proton has a kinetic energy EK. At this point, the alphaparticle has a kinetic energy
A.
.2KE
B. EK.
C. 2EK.
D. 4EK.(1)
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8. The diagram below illustrates some equipotential lines between two charged parallel metalplates.
0.1 m
+
– – – –
+ + +
80 V
60 V
40 V
20 V
The electric field strength between the plates is
A. 6 N C–1.
B. 8 N C–1.
C. 600 N C–1.
D. 800 N C–1.(1)
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9. The diagram below shows some equipotential lines in an electric field.
+300 V +290 V +280 V +270 V +260 V +250 V
X Y
The magnitude of the electric field strength at X is EX and at Y is EY.
Which one of the following correctly compares EX and EY and gives the correct direction of theelectric field?
Magnitude of field strengths Direction of field
A. EX EY X Y
B. EX EY Y X
C. EX EY X Y
D. EX EY Y X
(1)
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10. Three equal point charges X, Y and Z are fixed in the positions shown.
Z q3
1.0 m
X 1.0 m
90Y
q1
q2
The distance between q1 and q2 and the distance between q2 and q3 is 1.0 m. The electric forcebetween the charges at X and Y is F. The electric force between the charges at X and Z is
A.
.2
F
B.
.2
F
C. F.
D. 2F.(1)
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11. A proton of mass m and charge e is accelerated from rest through a potential difference V. Thefinal speed of the proton is
A.
.2
m
Ve
B.
.2
m
Ve
C.
.m
Ve
D.
.m
Ve
(1)
12. Which of the following correctly describes the nature of electric potential and electric fieldstrength?
Potential Field strength
A. Scalar Scalar
B. Scalar Vector
C. Vector Scalar
D. Vector Vector
(1)
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13. Which one of the following statements about electric potential gradient is correct?
A. Electric potential gradient is numerically equal to the gradient of the electric field.
B. Electric potential gradient at a point is numerically equal to the electric field strength atthat point.
C. When one joule of work is done in moving one coulomb of charge between two points,the electric potential gradient between the points is one volt per metre.
D. When one joule of work is done in moving one coulomb of charge to a point, the electricpotential gradient at that point is one volt per metre.
(1)
14. Four point charges of equal magnitude Q are placed at the corners of a square as shown below.The centre of the square is at the origin of the x-axis and the y-axis.
+Qy
–Q
x
+Q –Q
At which position, or positions, is the electric potential due to the four point charges equal tozero?
A. At the centre of the square only.
B. Along the x-axis only.
C. Along the y-axis only.
D. Along the x-axis and the y-axis.(1)
11
15. An electron and a proton are accelerated from rest through potential differences of the samemagnitude. After acceleration the speed of the electron is ve and the speed of the proton is vp.
Which of the following is the best estimate for the ratio
?e
p
v
v
A. 2000
B. 2000
C. 2000
1
D. 2000
1
(1)
12
16. A charged particle P is accelerated between two charged metal plates X and Y separated by adistance d. The particle starts from rest at plate X.
.
plate X plate Y
P
d
The kinetic energy of P, when it reaches plate Y, is K. The magnitude of the charge on P is e.
The magnitude of the electric field strength between the plates is
A.
.K
de
B.
.Ke
d
C.
.ed
K
D.
.d
Ke
(1)
13
17. X and Y are two points in an electric field. The potentials at X and Y are VX and VY
respectively where VX VY. A small, positive test charge +q is placed at X.
Which of the following is the work done per unit charge by the electric field on the charge asthe charge moves from point X to point Y?
A. YX VV
B. YX VV
C.
q
VV YX
D.
q
VV YX
(1)
18. Which of the following is the correct value of the electronvolt, measured in SI Units?
A. 1.6 10–19 N
B. 1.6 10–19 J
C. 9.1 10–31 N
D. 9.1 10–31 J(1)
14
19. The diagram below shows some lines of equipotential in the region of an electric field.
X Y
Which graph best shows the magnitude E of the electric field strength along the line XY?
E
X Yposition
A. B.
C. D.E
X Yposition
E
X Yposition
E
X Yposition
(1)
15
20. The work done on a positive point charge of magnitude 3.0 nC as it is moved at constant speedfrom one point to another is 12 nJ. The potential difference between the two points is
A. 0.0 V.
B. 0.25 V.
C. 4.0 V.
D. 36 V.(1)
21. A neutral conducting sphere is placed far away from a smaller, positively charged conductingsphere. The spheres are joined for a short period of time by a metallic wire.
How do the charge and the electric potential of the spheres compare after the wire is removed?
Charge Electric Potential
A. different different
B. different same
C. same different
D. same same
(1)
22. A proton and an alpha particle are accelerated from rest through the same potential difference.
After acceleration the ratio
isproton ofenergy kinetic
particle alpha ofenergy kinetic
A. .2
B. 2.
C. .22
D. 4.(1)
16
23. Two charged plastic balls are separated by a distance d in a vertical insulating tube, as shown.
d
tube
balls
The charge on each ball is doubled.
Coulomb’s law applies to the force between the balls and friction with the walls of the tube isnegligible.
What is now the separation of the balls?
A. 2
d
B. d
C. 2d
D. 4d(1)
24. This question is about electric fields.
(a) Define electric field strength.
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(b) An isolated metal sphere of radius 50.0 cm has a positive charge. On the diagram belowdraw lines to represent the electric field outside the sphere.
50.0 cmmetal sphere
(2)(Total 4 marks)
25. This question is about electric charge at rest.
(a) Define electric field strength at a point in an electric field.
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Four point charges of equal magnitude, are held at the corners of a square as shown below.
2a
2a
+Q+Q
–Q–Q
P
The length of each side of the square is 2a and the sign of the charges is as shown. The point Pis at the centre of the square.
(b) (i) Deduce that the magnitude of the electric field strength at point P due to one of the
point charges is equal to
.22a
kQ
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(ii) On the diagram above, draw an arrow to represent the direction of the resultantelectric field at point P.
(1)
(iii) Determine, in terms of Q, a and k, the magnitude of the electric field strength atpoint P.
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(Total 8 marks)
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26. Magnetic and electric fields
A proton is accelerated from rest in a vacuum through a potential difference of 420 V. Theproton then enters a region ABCD of uniform magnetic field as shown.
path of proton
A B
CD
The magnetic field is directed into the plane of the paper. The field strength is 15 mT.
(a) (i) Calculate the speed of the proton as it enters the region of the magnetic field.
.........................................................................................................................
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(ii) The path of the proton as drawn on the diagram is in the plane of the paper. Theproton enters the region ABCD of the magnetic field and leaves through the sideBC. On the diagram above, draw the path of the proton within and beyond theregion ABCD of the magnetic field. Label the path P.
(2)
(iii) Determine the magnitude of the force due to the magnetic field that acts on theproton while the proton is in the region ABCD.
.........................................................................................................................
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(b) (i) Define electric field strength at a point.
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(ii) Determine the magnitude of the electric field strength that would produce a forceon a proton that is equal to the force calculated in (a)(iii).
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(iii) The electric field calculated in (b)(ii) is applied in the region ABCD. The electricfield is arranged such that, when a proton enters the region, the force due to theelectric field is opposite in direction to the force due to the magnetic field.Suggest, with a reason, the path that the proton will follow in the region ABCD.
.........................................................................................................................
.........................................................................................................................(2)
(Total 12 marks)
27. This question is about the electric field due to a charged sphere and the motion of electrons inthat field.
The diagram below shows an isolated, metal sphere in a vacuum that carries a negative electriccharge of 9.0 nC.
–
21
(a) On the diagram draw arrows to represent the electric field pattern due to the chargedsphere.
(3)
(b) The electric field strength at the surface of the sphere and at points outside the sphere canbe determined by assuming that the sphere acts as though a point charge of magnitude
9.0 nC is situated at its centre. The radius of the sphere is 4.5 × 10–2 m. Deduce that the
magnitude of the field strength at the surface of the sphere is 4.0 × 104 Vm–1.
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An electron is initially at rest on the surface of the sphere.
(c) (i) Describe the path followed by the electron as it leaves the surface of the sphere.
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(ii) Calculate the initial acceleration of the electron.
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(iii) State and explain whether the acceleration of the electron remains constant,increases or decreases as it moves away from the sphere.
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(iv) At a certain point P, the speed of the electron is 6.0 × 106 ms–1. Determine thepotential difference between the point P and the surface of the sphere.
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(Total 13 marks)
28. This question is about the electric potential due to a charged sphere.
(a) Define electric potential at a point in an electric field.
.....................................................................................................................................
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The diagram below shows an isolated, metal sphere in a vacuum that carries a negative electriccharge of 9.0 nC.
–
(b) On the diagram above draw
(i) arrows to represent the electric field pattern in the region outside the chargedsphere.
(3)
(ii) lines to represent three equipotential surfaces in the region outside the sphere. Thepotential differences between the lines are to be equal in value.
(2)
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(c) Explain how the lines representing the equipotential surfaces that you have sketchedindicate that the strength of the electric field is decreasing with distance from the centreof the sphere.
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(d) The electric field strength at all points inside the conductor is zero. On the axes below,draw a graph to show the variation with distance r from the centre of the sphere of thepotential V. The dotted line is drawn at r = a where a is the radius of the sphere. (Note:this is a sketch graph; you do not need to add values to the axes.)
00
V
ra
(2)
(e) The electric field strength at the surface of the sphere and at points outside the spheremay be determined by assuming that the sphere acts as though a point charge of
magnitude 9.0 nC is situated at its centre. The radius of the sphere is 4.5 × 10–2 m.Deduce that the potential at the surface of the sphere is –1800 V.
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An electron is initially at rest at the surface of the sphere.
(f) (i) Describe the path followed by the electron as it leaves the surface of the sphere.
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(ii) Determine the speed of the electron when it reaches a point a distance 0.30 m fromthe centre of the sphere.
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(Total 18 marks)
29. This question is about aspects of electric fields and electric charge.
(a) A proton may be considered to be a point charge. For such a proton
(i) sketch the electric field pattern.
(2)
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(ii) calculate the magnitude of the electric field strength at a distance of 5.0×10–11 mfrom the proton.
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(b) In a simple model of the hydrogen atom, an electron orbits the proton. Both electron and
proton are regarded as point charges. The orbital radius of the electron is 5.0×10–11 m.
(i) Using your answer to (a)(ii) deduce that the magnitude of the electric force
between the electron and the proton is 9.3×10–8N.
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(ii) Deduce that the kinetic energy of the electron is 2.3×10–18 J.
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(c) The electron in (b) also has electrostatic potential energy.
(i) Define electrostatic potential at a point.
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(ii) Calculate the electrostatic potential energy of this electron.
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(d) Using your answers in (b)(ii) and (c)(ii) determine the energy required, in electron volt,to completely remove the electron from the influence of the proton.
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Fields and electric charge in conductors
(e) Define electromotive force (e.m.f.).
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(f) A filament lamp is operating at normal brightness.
The potential difference across the lamp is 6.0 V. The current in the filament is 0.20 A.For the filament of this lamp, calculate
(i) the resistance.
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(ii) the power dissipated.
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(g) The lamp in (f) is connected in the circuit below. The lamp is still operating at normalbrightness.
BR
The battery B has an internal resistance of 5.0 and the resistance R of the resistor is 15.
(i) Calculate the current in the resistor R.
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(ii) Determine the e.m.f. of the battery.
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(Total 22 marks)
30. Fields and potential
Electric fields and potential
(a) Define electric potential.
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An isolated metal sphere of radius 50.0 cm has a positive charge. The electric potential at thesurface of the sphere is 6.0 V.
50.0 cmmetal sphere
(b) (i) On the diagram above, draw a line to represent an equipotential surface outside thesphere.
(1)
(ii) On the axes below, draw a sketch graph to show how the potential V outside thesphere varies with distance r from the surface of the sphere.
V / V
6
4
2
0 0.0 0.5 1.0 1.5 r / m
(4)
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(iii) Explain how the graph drawn in (b) (ii) can be used to determine the magnitude ofthe electric field strength at the surface of the sphere.
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(c) On the diagram below draw lines to represent the electric field outside the sphere.
50.0 cmmetal sphere
(2)
Gravitational fields and potential
(d) Derive an expression for the gravitational field strength as a function of distance awayfrom a point mass M.
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(e) The radius of the Earth is 6400 km and the gravitational field strength at its surface is 9.8N kg–1. Calculate a value for the mass of the Earth.
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(f) On the diagram below draw lines to represent the gravitational field outside the Earth.
(2)
(g) A satellite that orbits the Earth is in the gravitational field of the Earth. Discuss why anastronaut inside the satellite feels weightless.
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(h) The gravitational potential outside the Earth and the electric potential outside the sphereboth vary with distance. Compare these variations.
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(Total 23 marks)
31. This question is about forces on charged particles.
(a) A charged particle is situated in a field of force. Deduce the nature of the force-field(magnetic, electric or gravitational) when the force on the particle
(i) is along the direction of the field regardless of its charge and velocity;
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(ii) is independent of the velocity of the particle but depends on its charge;
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(iii) depends on the velocity of the particle and its charge.
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(b) An electron is accelerated from rest in a vacuum through a potential difference of 2.1 kV.
Deduce that the final speed of the electron is 2.7 × 107 m s–1.
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The electron in (b) then enters a region of uniform electric field between two conductinghorizontal metal plates as shown below.
Path ofelectron P
2.7 × 10 m s–17
+95 V
2.2 cm
0 V12 cm
The electric field outside the region of the plates may be assumed to be zero. The potentialdifference between the plates is 95 V and their separation is 2.2 cm.
As the electron enters the region of the electric field, it is travelling parallel to the plates.
(c) (i) On the diagram above, draw an arrow at P to show the direction of the force due tothe electric field acting on the electron.
(1)
(ii) Calculate the force on the electron due to the electric field.
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(d) The plates in the diagram above are of length 12 cm. Determine
(i) the time of flight between the plates.
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(ii) the vertical distance moved by the electron during its passage between the plates.
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(e) Suggest why gravitational effects were not considered when calculating the deflection ofthe electron.
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(f) In a mass spectrometer, electric and magnetic fields are used to select charged particlesof one particular speed. A uniform magnetic field is applied in the region between theplates, such that the electron passes between the plates without being deviated.
For this magnetic field,
(i) state and explain its direction;
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(ii) determine its magnitude.
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(g) The electric and magnetic fields in (f) remain unchanged. Giving a brief explanation ineach case, compare qualitatively the deflection of the electron in (f) with that of
(i) an electron travelling at a greater initial speed;
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(ii) a proton having the same speed;
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(iii) an alpha particle (α-particle) having the same speed.
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(Total 30 marks)
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