ECAT — Engineering College Admission Test (UET)

ECAT Physics — Magnetism, Electromagnetic Induction and AC (Set 4)

Take the ECAT Physics — Magnetism, Electromagnetic Induction and AC (Set 4): 30 multiple-choice questions (40 minutes) with instant scoring and a full…

What this test covers

30 ECAT Physics

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

Q1. Two long parallel wires 10 cm apart carry currents of 10 A and 5 A in the same direction. The force per metre of length between them is
- A. 1 × 10⁻⁵ N/m, attractive
- B. 2 × 10⁻⁴ N/m, attractive
- C. 1 × 10⁻⁴ N/m, attractive ✓
- D. 1 × 10⁻⁴ N/m, repulsive
Answer: C. 1 × 10⁻⁴ N/m, attractive
Explanation: F/L = μ₀I₁I₂/2πd = (2 × 10⁻⁷)(10)(5)/0.1 = 1 × 10⁻⁴ N/m. Parallel currents attract.
Q2. A circular coil of 10 turns and radius 0.2 m carries a current of 2 A. The magnetic field at its centre is
- A. π × 10⁻⁵ T
- B. 2π × 10⁻⁵ T ✓
- C. 4π × 10⁻⁵ T
- D. 2π × 10⁻⁶ T
Answer: B. 2π × 10⁻⁵ T
Explanation: B = μ₀NI/2R = (4π × 10⁻⁷)(10)(2)/(2 × 0.2) = 2π × 10⁻⁵ T.
Q3. Two long straight parallel wires 20 cm apart carry 5 A in opposite directions. The magnetic field at the point midway between them is
- A. 4 × 10⁻⁵ T
- B. zero
- C. 2 × 10⁻⁵ T ✓
- D. 1 × 10⁻⁵ T
Answer: C. 2 × 10⁻⁵ T
Explanation: Each wire gives μ₀I/2πr = (2 × 10⁻⁷)(5)/0.1 = 10⁻⁵ T. For opposite currents the fields are in the same direction at the midpoint, so they add: 2 × 10⁻⁵ T.
Q4. Singly ionised neon-20 and neon-22 ions are accelerated through the same potential difference and then enter the same uniform magnetic field at right angles. The ratio of the radii of their circular paths (Ne-22 : Ne-20) is
- A. √(11/10) ✓
- B. 11/10
- C. 10/11
- D. √(10/11)
Answer: A. √(11/10)
Explanation: r = mv/qB = √(2mV/q)/B ∝ √m for equal charge. The ratio is √(22/20) = √(11/10).
Q5. A charged particle enters a uniform magnetic field with velocity at 45° to the field. The ratio of the pitch of its helical path to the radius of the helix is
- A. 2π ✓
- B. π
- C. π/2
- D. 2π/√2
Answer: A. 2π
Explanation: Pitch = 2πm(v cos45°)/qB and radius = m(v sin45°)/qB. Their ratio is 2π cot45° = 2π.

The other 25 questions

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Q6. A charge of 0.5 C moves with velocity (3î + 4ĵ) m/s in a magnetic field 2k̂ T. The magnitude of the magnetic force on it is
- A. 7 N
- B. 10 N
- C. 2.5 N
- D. 5 N
Q7. A coil of 100 turns and area 0.02 m² carries 2 A in a uniform field of 0.5 T. The plane of the coil makes 30° with the field direction. The torque on the coil is
- A. √3 N m
- B. 2 N m
- C. 0.5 N m
- D. 1 N m
Q8. A galvanometer has resistance 90 Ω. What resistance must be connected in parallel with it so that only 10% of the total current passes through the galvanometer?
- A. 81 Ω
- B. 9 Ω
- C. 1 Ω
- D. 10 Ω
Q9. A coil of 200 turns and area 0.01 m² has its plane perpendicular to a magnetic field that grows uniformly from 0.2 T to 0.8 T in 0.3 s. The induced emf is
- A. 1.2 V
- B. 0.4 V
- C. 4 V
- D. 2 V
Q10. A rod 0.5 m long moves at 4 m/s perpendicular to a 0.3 T field on frictionless rails joined by a 0.2 Ω resistor (rails and rod otherwise have no resistance). The force needed to keep it moving at constant speed is
- A. 0.225 N
- B. 0.45 N
- C. 0.9 N
- D. 0.6 N
Q11. A strong magnet dropped through a long vertical copper tube falls much more slowly than in free fall. This happens because
- A. air resistance inside the narrow tube increases greatly
- B. the non-magnetic tube shields the magnet from gravity
- C. copper attracts the magnet upward with a steady force
- D. eddy currents induced in the tube oppose the magnet’s motion
Q12. A long air-core solenoid has 1000 turns, length 0.5 m and cross-sectional area 5 × 10⁻⁴ m². Its self-inductance is
- A. 4π × 10⁻⁷ H
- B. 2π × 10⁻⁴ H
- C. 8π × 10⁻⁴ H
- D. 4π × 10⁻⁴ H
Q13. Two coils have mutual inductance 0.4 H. The current in the primary falls uniformly from 5 A to zero in 0.1 s. The emf induced in the secondary is
- A. 2 V
- B. 50 V
- C. 20 V
- D. 0.2 V
Q14. An inductor of 2 H and resistance 4 Ω is connected to a 12 V battery. The energy stored in the inductor when the current has reached its steady value is
- A. 36 J
- B. 18 J
- C. 9 J
- D. 3 J
Q15. A step-down transformer is 80% efficient. Its secondary delivers 20 V across a 10 Ω load while its primary is connected to a 200 V supply. The current drawn by the primary is
- A. 0.1 A
- B. 0.25 A
- C. 0.4 A
- D. 0.2 A
Q16. A half-wave rectified current has peak value I₀ (it is zero for the other half of each cycle). Its rms value is
- A. 2I₀/π
- B. I₀/√2
- C. I₀/2
- D. I₀/π
Q17. The current in a circuit is i = 3 + 4 sin ωt amperes. Its rms value is
- A. √17 A
- B. 5 A
- C. 7 A
- D. √41 A
Q18. A capacitor of 100/π μF is connected to a 50 Hz AC supply. Its capacitive reactance is
- A. 200 Ω
- B. 50 Ω
- C. 100 Ω
- D. 10 Ω
Q19. In a series circuit, R = 30 Ω, X_L = 70 Ω and X_C = 30 Ω. The impedance of the circuit is
- A. 70 Ω
- B. 130 Ω
- C. 50 Ω
- D. 100 Ω
Q20. A series circuit has R = 10 Ω, L = 1 H and C = 100 μF and is driven at its resonant frequency by a source of 5 V rms. The rms voltage across the inductor is
- A. 5 V
- B. 0 V
- C. 500 V
- D. 50 V
Q21. A 100 V rms AC source drives a series R–L circuit with R = 30 Ω and X_L = 40 Ω. The average power dissipated is
- A. 160 W
- B. 120 W
- C. 80 W
- D. 200 W
Q22. Which of these draws no net power over a complete cycle when connected to an AC source?
- A. An ideal inductor
- B. A resistor
- C. A heating element
- D. A filament lamp
Q23. A 50-turn coil of area 0.2 m² rotates at 50 revolutions per second in a uniform field of 0.1 T. The peak emf generated is
- A. 200π V
- B. 50π V
- C. 100π V
- D. 100 V
Q24. A DC motor has armature resistance 2 Ω and runs on 120 V. When running normally the back emf is 100 V. The ratio of the starting current to the running current is
- A. 6
- B. 1.2
- C. 5
- D. 12
Q25. The iron core of a transformer is made of thin insulated laminations instead of a solid block in order to
- A. increase the flux leakage from the core
- B. reduce the energy loss due to eddy currents
- C. increase the hysteresis loss in the core
- D. reduce the number of turns needed in the coils
Q26. A square loop of area 0.04 m² is in a uniform field of 0.5 T with its plane making an angle of 30° to the field. The magnetic flux through it is
- A. 1.0 × 10⁻² Wb
- B. 1.7 × 10⁻² Wb
- C. 2.5 × 10⁻³ Wb
- D. 2.0 × 10⁻² Wb
Q27. A long straight cylindrical conductor of radius R carries a steady current uniformly spread over its cross-section. The ratio of the magnetic field at a distance R/2 from its axis to that at its surface is
- A. 1
- B. 1/4
- C. 1/2
- D. 2
Q28. The magnetic flux through a closed coil of resistance 5 Ω changes from 0.04 Wb to 0.01 Wb. The total charge that flows through the coil is
- A. 1.5 × 10⁻³ C
- B. 6 × 10⁻³ C
- C. 0.15 C
- D. 6 × 10⁻² C
Q29. In an AC circuit containing only a capacitor, at the instant the current through it is at its maximum value, the voltage across the capacitor is
- A. equal to the rms voltage
- B. at its maximum value
- C. half its maximum value
- D. zero
Q30. A charged particle moves at right angles to a uniform magnetic field in a circle. If its speed is doubled, the time taken for one revolution
- A. is doubled
- B. remains the same
- C. is halved
- D. becomes four times