A Multiple Choice — 20 questions (20 marks)
IQ1 — Electric and Magnetic Fields
Question 1
Two point charges of $+4.0 \\mu$C and $+6.0 \\mu$C are placed 0.20 m apart in vacuum. What is the magnitude of the electrostatic force between them?
A 2.7 N
B 5.4 N
C 5.4 N ($F = k\\dfrac{q_1 q_2}{r^2} = 8.99\\times10^9 \\times \\dfrac{(4.0\\times10^{-6})(6.0\\times10^{-6})}{0.20^2}$)
D 10.8 N
Correct: C. $F = kq_1q_2/r^2 = 8.99\\times10^9 \\times 24\\times10^{-12}/0.04 = 5.39$ N $\\approx$ 5.4 N. The force is repulsive because both charges are positive.
Question 2
An electron moves at $3.0\\times10^6$ m/s perpendicular to a uniform magnetic field of 0.20 T. What is the radius of its circular path?
A $4.3\\times10^{-5}$ m
B $8.5\\times10^{-5}$ m ($r = mv/qB = 9.11\\times10^{-31} \\times 3.0\\times10^6 / (1.6\\times10^{-19} \\times 0.20)$)
C $1.7\\times10^{-4}$ m
D $3.4\\times10^{-4}$ m
Correct: B. $r = mv/(qB) = 9.11\\times10^{-31} \\times 3.0\\times10^6 / (1.6\\times10^{-19} \\times 0.20) = 8.5\\times10^{-5}$ m. The magnetic force provides centripetal force for circular motion.
Question 3
Which statement correctly compares electric and magnetic forces on charged particles?
A Both forces do work on the particle
B Neither force can do work
C Magnetic force can do work; electric force cannot
D Electric force can do work; magnetic force cannot (it is always perpendicular to velocity)
Correct: D. Electric force $\\vec{F}_E = q\\vec{E}$ can have a component parallel to displacement, so it can do work. Magnetic force $\\vec{F}_B = q\\vec{v} \\times \\vec{B}$ is always perpendicular to velocity, so $W = \\vec{F} \\cdot \\vec{d} = 0$.
Question 4
An electron is accelerated from rest through a potential difference of 500 V. What is its final speed?
A $1.3\\times10^7$ m/s ($v = \\sqrt{2qV/m}$)
B $4.0\\times10^6$ m/s
C $1.0\\times10^7$ m/s
D $2.0\\times10^7$ m/s
Correct: A. $\\Delta K = qV = 1.6\\times10^{-19} \\times 500 = 8.0\\times10^{-17}$ J. $v = \\sqrt{2K/m} = \\sqrt{2 \\times 8.0\\times10^{-17}/9.11\\times10^{-31}} = 1.3\\times10^7$ m/s.
Question 5
Two parallel plates 0.020 m apart have a potential difference of 400 V. The electric field between them is:
A $8.0\\times10^{-5}$ N/C
B 2000 N/C
C $2.0\\times10^4$ N/C ($E = V/d = 400/0.020$)
D $8.0\\times10^3$ N/C
Correct: C. $E = V/d = 400/0.020 = 2.0\\times10^4$ N/C. The field is uniform between parallel plates.
IQ2 — The Motor Effect
Question 6
A 0.30 m wire carries 5.0 A perpendicular to a uniform magnetic field of 0.40 T. The force on the wire is:
A 0.30 N
B 0.60 N ($F = BIL = 0.40 \\times 5.0 \\times 0.30$)
C 1.5 N
D 6.0 N
Correct: B. $F = BIL = 0.40 \\times 5.0 \\times 0.30 = 0.60$ N. Direction is found using the right-hand palm rule.
Question 7
Two parallel wires carry currents in opposite directions. The force between them is:
A Repulsive
B Attractive
C Zero
D Parallel to the wires
Correct: A. Opposite currents produce repulsive forces. Each wire sits in the magnetic field of the other, and the motor effect forces point away from each other.
Question 8
A coil with 50 turns and area $4.0\\times10^{-3}$ m² carries 3.0 A in B = 0.30 T. Maximum torque is:
A 0.090 N m
B 0.12 N m
C 0.15 N m
D 0.18 N m ($\\tau = nBIA = 50 \\times 0.30 \\times 3.0 \\times 4.0\\times10^{-3}$)
Correct: D. $\\tau_{max} = nBIA = 50 \\times 0.30 \\times 3.0 \\times 4.0\\times10^{-3} = 0.18$ N m. Maximum when coil plane is parallel to B.
Question 9
A DC motor connected to 18 V has coil resistance 3.0 ohms. At full speed, back emf is 15 V. The running current is:
A 6.0 A
B 5.0 A
C 1.0 A ($I = (18-15)/3.0$)
D 11 A
Correct: C. $I = (V - \\varepsilon_{back})/R = (18 - 15)/3.0 = 1.0$ A. Back emf reduces the net voltage driving current.
Question 10
The torque on a coil is zero when the coil plane is:
A Parallel to the magnetic field
B Perpendicular to the magnetic field
C At 45 degrees to the field
D Rotating at maximum angular velocity
Correct: B. $\\tau = nBIA \\cos \\theta$ where $\\theta$ is the angle between the coil plane and B. When perpendicular, $\\theta = 90°$ and $\\cos 90° = 0$.
IQ3 — Electromagnetic Induction
Question 11
A coil of 150 turns experiences a flux change from 0.010 Wb to 0.050 Wb in 0.10 s. The average induced emf is:
A 30 V
B 60 V ($\\varepsilon = 150 \\times 0.040/0.10$)
C 120 V
D 600 V
Correct: B. $\\varepsilon = N \\Delta\\Phi/\\Delta t = 150 \\times (0.050-0.010)/0.10 = 150 \\times 0.040/0.10 = 60$ V.
Question 12
Lenz's Law ensures that:
A The induced current opposes the change in flux
B The induced current reinforces the change in flux
C Energy is not conserved in electromagnetic systems
D The magnetic field always increases
Correct: A. Lenz's Law states the induced current creates a magnetic field that opposes the change in flux that produced it. This is required by conservation of energy.
Question 13
A transformer has 300 primary turns and 900 secondary turns. If Vp = 120 V, the secondary voltage is:
A 40 V
B 120 V
C 360 V ($V_s = 120 \\times 900/300$)
D 480 V
Correct: C. $V_s/V_p = N_s/N_p$, so $V_s = 120 \\times 900/300 = 360$ V. This is a step-up transformer.
Question 14
The peak emf of an AC generator with n = 80, B = 0.40 T, A = 5.0x10^-3 m², omega = 100 rad/s is:
A 8.0 V
B 16 V ($\\varepsilon_0 = 80 \\times 0.40 \\times 5.0\\times10^{-3} \\times 100$)
C 32 V
D 160 V
Correct: B. $\\varepsilon_0 = NBA\\omega = 80 \\times 0.40 \\times 5.0\\times10^{-3} \\times 100 = 16$ V. Emf varies sinusoidally with time.
Question 15
A conducting rod of length 0.25 m moves at 8.0 m/s perpendicular to B = 0.50 T. The induced emf is:
A 1.0 V ($\\varepsilon = Blv = 0.50 \\times 0.25 \\times 8.0$)
B 2.0 V
C 4.0 V
D 16 V
Correct: A. $\\varepsilon = Blv = 0.50 \\times 0.25 \\times 8.0 = 1.0$ V. This is motional emf from cutting magnetic field lines.
IQ4 — Applications of Electromagnetism
Question 16
A 6-pole induction motor on 50 Hz has synchronous speed:
A 3000 RPM
B 1000 RPM ($n_s = 120 \\times 50 / 6$)
C 1500 RPM
D 500 RPM
Correct: B. $n_s = 120f/p = 120 \\times 50 / 6 = 1000$ RPM. The rotor turns slightly slower due to slip.
Question 17
In a velocity selector with E = 3000 V/m and B = 0.20 T, the speed of undeflected ions is:
A $6.0\\times10^2$ m/s
B $6.0\\times10^3$ m/s
C $1.5\\times10^4$ m/s ($v = E/B = 3000/0.20$)
D $6.0\\times10^4$ m/s
Correct: C. When $qE = qvB$, the charge cancels, giving $v = E/B = 3000/0.20 = 1.5\\times10^4$ m/s.
Question 18
Magnetic braking is smooth and wear-free because:
A There is no physical contact between components
B It uses friction pads
C It requires hydraulic fluid
D It relies on air resistance
Correct: A. Eddy currents induced in a conducting disc or rail create an opposing magnetic field (Lenz's Law). This provides contactless braking with no mechanical wear.
Question 19
Power is transmitted at high voltage to:
A Increase the current in the lines
B Reduce the resistance of the lines
C Make transformers unnecessary
D Reduce power loss ($P_{loss} = I^2 R$) for the same transmitted power
Correct: D. For fixed power P = VI, increasing V decreases I. Since $P_{loss} = I^2 R$, lower current dramatically reduces resistive losses in transmission lines.
Question 20
In a mass spectrometer, ions with larger mass-to-charge ratio:
A Have smaller radius of curvature
B Have larger radius of curvature ($r = mv/qB$)
C Experience less magnetic force
D Travel faster through the velocity selector
Correct: B. After the velocity selector, all ions have the same speed. In the magnetic field, $r = mv/qB$, so larger m/q gives larger radius. This separates ions by mass.
B Extended Response — 4 questions (45 marks)
(a) An electron is accelerated from rest through a potential difference of 2000 V. Calculate its final speed. ($m_e = 9.11\\times10^{-31}$ kg) (2 marks)
(b) The electron then enters a uniform magnetic field of 0.30 T perpendicular to its velocity. Calculate the radius of its circular path. (2 marks)
(c) Explain how a mass spectrometer uses crossed electric and magnetic fields to select ions of a specific velocity, and why this velocity selection is independent of charge and mass. (4 marks)
(a) A rectangular coil with 60 turns and area $5.0\\times10^{-3}$ m² carries 4.0 A in a uniform magnetic field of 0.25 T. Calculate the maximum torque on the coil. (2 marks)
(b) The coil is used as the armature of a DC motor connected to a 20 V supply. The coil resistance is 2.0 ohms. Calculate the starting current and the back emf when the running current is 2.0 A. (3 marks)
(c) Explain the role of the split-ring commutator and the radial magnetic field in maintaining continuous rotation of a DC motor. (4 marks)
(d) Compare and contrast DC motors and AC induction motors, referring to commutators, brushes, and slip. (3 marks)
(a) A coil of 100 turns and area $2.0\\times10^{-3}$ m² rotates at 50 Hz in a uniform magnetic field of 0.40 T. Calculate the maximum emf generated. Sketch a graph of emf versus time for one complete cycle, labelling the maximum value and the period. (4 marks)
(b) A transformer has 200 primary turns and 1000 secondary turns. The primary is connected to 240 V AC and draws 5.0 A. Assuming an ideal transformer, calculate the secondary voltage and current. (3 marks)
(c) Explain why transformers only work with AC, and describe how laminated cores reduce energy losses. (3 marks)
(d) A bar magnet is dropped through a copper tube. Explain why it falls more slowly than through a PVC tube of the same dimensions. (2 marks)
(a) A power station generates 500 MW at 25 kV. This is stepped up to 500 kV for transmission through lines with total resistance 2.0 ohms. Calculate: (i) the current in the transmission lines, (ii) the power loss in the lines, (iii) the percentage power loss. (4 marks)
(b) Explain why increasing transmission voltage reduces power loss, and describe the role of step-up and step-down transformers in the electricity grid. (4 marks)
(c) In a mass spectrometer, singly charged ions of mass $2.0\\times10^{-26}$ kg are accelerated through 5000 V and then enter a uniform magnetic field of 0.50 T perpendicular to their velocity. Calculate the radius of their circular path. (3 marks)
(d) Describe one application of eddy currents other than magnetic braking, and explain the physics principle involved. (2 marks)