ECAT — Engineering College Admission Test (UET)

ECAT Physics — Magnetism, Electromagnetic Induction and AC (Set 5)

Take the ECAT Physics — Magnetism, Electromagnetic Induction and AC (Set 5): 30 multiple-choice questions (40 minutes) with instant scoring and a full…

What this test covers

Sample questions with answers

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

  1. Q1. A wire bent into a semicircle of diameter 0.4 m carries a current of 5 A. It lies in a plane perpendicular to a uniform magnetic field of 0.1 T. The net magnetic force on the wire is:

    • A. 0.63 N
    • B. 0.2 N ✓
    • C. 0.31 N
    • D. 0.1 N

    Answer: B. 0.2 N

    Explanation: The force on a curved wire equals that on the straight chord joining its ends: F = BIL = 0.1 × 5 × 0.4 = 0.2 N.

  2. Q2. Two long straight parallel wires 8 cm apart carry currents of 6 A and 2 A in opposite directions. The net magnetic field is zero on the line through the wires at a point that is:

    • A. 4 cm beyond the 2 A wire, away from the 6 A wire ✓
    • B. 4 cm beyond the 6 A wire, away from the 2 A wire
    • C. 2 cm from the 2 A wire, between the wires
    • D. 6 cm beyond the 2 A wire, away from the 6 A wire

    Answer: A. 4 cm beyond the 2 A wire, away from the 6 A wire

    Explanation: Between opposite currents the fields add, so zero field lies outside, nearer the smaller current. With x from the 2 A wire: 6/(x + 8) = 2/x, so 6x = 2x + 16 and x = 4 cm.

  3. Q3. A circular coil of 20 turns and radius 5 cm carries a current of 2.5 A. The magnetic field at its centre is:

    • A. 4π × 10⁻⁴ T
    • B. π × 10⁻⁴ T
    • C. 2π × 10⁻⁴ T ✓
    • D. 2π × 10⁻³ T

    Answer: C. 2π × 10⁻⁴ T

    Explanation: B = μ₀NI/2r = (4π×10⁻⁷)(20)(2.5)/(2 × 0.05) = 2π × 10⁻⁴ T.

  4. Q4. A proton and an α-particle (mass 4 times, charge 2 times the proton's) enter the same uniform magnetic field perpendicular to it with the same kinetic energy. The ratio of the radii of their circular paths, r_p : r_α, is:

    • A. 1 : 1 ✓
    • B. 2 : 1
    • C. 1 : 4
    • D. 1 : 2

    Answer: A. 1 : 1

    Explanation: r = √(2mK)/(qB). For α: √(4)/2 = 1 times the proton's value, so r_p : r_α = 1 : 1.

  5. Q5. A proton (charge 1.6 × 10⁻¹⁹ C, mass 1.67 × 10⁻²⁷ kg) circulates in a uniform field of 0.5 T. Its orbital frequency is approximately:

    • A. 76 MHz
    • B. 15 MHz
    • C. 4.8 MHz
    • D. 7.6 MHz ✓

    Answer: D. 7.6 MHz

    Explanation: f = qB/2πm = (1.6×10⁻¹⁹ × 0.5)/(2π × 1.67×10⁻²⁷) ≈ 7.6 × 10⁶ Hz, independent of its speed.

The other 25 questions

Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.

  1. Q6. A particle of mass 1.6 × 10⁻²⁷ kg and charge 1.6 × 10⁻¹⁹ C moves at 2 × 10⁵ m s⁻¹ in a uniform field of 0.01 T, with its velocity at 30° to the field. The radius of the helical path is:

    • A. 0.1 m
    • B. 0.17 m
    • C. 0.05 m
    • D. 0.2 m
  2. Q7. An electron moving eastward enters a region with a magnetic field pointing north (take east = +x, north = +y, up = +z). The magnetic force on the electron points:

    • A. southward
    • B. westward
    • C. downward
    • D. upward
  3. Q8. A rectangular coil of 50 turns and area 0.04 m² carries 2 A in a uniform field of 0.5 T. The plane of the coil makes an angle of 30° with the field. The torque on the coil is:

    • A. 1.0 N m
    • B. 2.0 N m
    • C. 0.87 N m
    • D. 1.73 N m
  4. Q9. A coil of 100 turns and area 0.02 m² is in a uniform field of 0.5 T whose direction makes 60° with the normal to the coil. The magnetic flux linkage of the coil (NΦ) is:

    • A. 0.87 Wb
    • B. 5 mWb
    • C. 0.5 Wb
    • D. 1.0 Wb
  5. Q10. A 100-turn coil of area 0.01 m² has its plane perpendicular to a uniform field of 0.4 T. It is flipped through 180° in 0.2 s. The average emf induced in the coil is:

    • A. 4 V
    • B. 0.8 V
    • C. 2 V
    • D. 8 V
  6. Q11. A rod of length 0.5 m slides at a constant speed of 4 m s⁻¹ on horizontal rails joined by a 2 Ω resistor, in a vertical field of 0.5 T. Ignoring other resistance, the external force needed to keep it moving at constant speed is:

    • A. 0.25 N
    • B. 0.5 N
    • C. 0.125 N
    • D. 1 N
  7. Q12. A metal rod of length 1 m rotates about one end in a uniform magnetic field of 0.2 T perpendicular to its plane of rotation, at 10 rad s⁻¹. The emf between its ends is:

    • A. 0.5 V
    • B. 2 V
    • C. 1 V
    • D. 0.2 V
  8. Q13. A strong bar magnet is dropped vertically down the axis of a long vertical copper tube. Compared with free fall, the magnet falls:

    • A. more slowly, because induced eddy currents oppose its motion
    • B. at the same rate, because copper is non-magnetic
    • C. more slowly, because copper repels the magnet at rest
    • D. faster, because the copper attracts the magnet
  9. Q14. A long air-core solenoid has 500 turns, length 0.5 m and cross-sectional area 10⁻³ m². Its self-inductance is approximately:

    • A. 63 mH
    • B. 6.3 mH
    • C. 0.63 mH
    • D. 0.063 mH
  10. Q15. The current in the primary coil of a pair of coils changes at 4 A s⁻¹, and an emf of 2 V is induced in the secondary. The mutual inductance of the pair is:

    • A. 2 H
    • B. 0.5 H
    • C. 8 H
    • D. 0.25 H
  11. Q16. A power of 100 kW is sent along a line of total resistance 2 Ω, first at 2000 V and then at 20 000 V. The ratio of line power loss at 20 000 V to that at 2000 V is:

    • A. 1 : 1000
    • B. 1 : 100
    • C. 1 : 20
    • D. 1 : 10
  12. Q17. An alternating current is i = 10 sin(100πt) amperes, with t in seconds. The time taken, starting from zero, to reach its first peak value is:

    • A. 2.5 ms
    • B. 10 ms
    • C. 5 ms
    • D. 20 ms
  13. Q18. An alternating current has a peak value of 10 A. Its mean (average) value over one half cycle is approximately:

    • A. 10 A
    • B. 5 A
    • C. 7.1 A
    • D. 6.4 A
  14. Q19. A heater of resistance 5 Ω carries a sinusoidal alternating current of peak value 4 A. The average power dissipated is:

    • A. 56.6 W
    • B. 40 W
    • C. 80 W
    • D. 20 W
  15. Q20. A series circuit has R = 60 Ω, inductive reactance 130 Ω and capacitive reactance 50 Ω, and is connected to a 200 V rms supply. The average power dissipated in the circuit is:

    • A. 400 W
    • B. 160 W
    • C. 200 W
    • D. 240 W
  16. Q21. A series LCR circuit has L = 0.1 H, C = 10 μF and R = 10 Ω, and is driven at resonance by a 5 V (rms) source. The rms voltage across the inductor is:

    • A. 500 V
    • B. 50 V
    • C. 5 V
    • D. 100 V
  17. Q22. In a series circuit with R = 30 Ω, X_L = 50 Ω and X_C = 10 Ω, the phase relationship between the supply voltage and the current is:

    • A. current leads voltage by 53°
    • B. voltage leads current by 53°
    • C. voltage leads current by 37°
    • D. voltage leads current by 90°
  18. Q23. A pure inductor is connected to an AC source. The average power absorbed by the inductor over a complete cycle is:

    • A. ½V_rms I_rms
    • B. V_rms I_rms
    • C. zero
    • D. V_rms²/X_L
  19. Q24. The core of a transformer is built from thin insulated iron sheets pressed together instead of one solid block. This is mainly to reduce:

    • A. the voltage drop across the secondary load
    • B. energy loss due to eddy currents
    • C. energy loss in the copper windings
    • D. the magnetic flux produced
  20. Q25. A coil of 100 turns and area 0.05 m² rotates at 50 revolutions per second in a uniform field of 0.2 T. The rms value of the emf generated is approximately:

    • A. 314 V
    • B. 157 V
    • C. 222 V
    • D. 444 V
  21. Q26. A DC motor is connected to a 220 V supply and its armature resistance is 2 Ω. When running at full speed it draws 10 A. The current drawn at the instant of starting (armature at rest) would be:

    • A. 220 A
    • B. 110 A
    • C. 90 A
    • D. 10 A
  22. Q27. A DC motor of armature resistance 1 Ω connected to a 120 V supply draws 20 A while running. The mechanical power it develops is:

    • A. 2000 W
    • B. 2800 W
    • C. 2400 W
    • D. 400 W
  23. Q28. A closed loop encircles three long straight wires: two carrying 6 A and 1 A into the page and one carrying 3 A out of the page. The value of ∮B·dl around the loop (μ₀ = 4π × 10⁻⁷ T m A⁻¹) is:

    • A. 8π × 10⁻⁷ T m
    • B. 24π × 10⁻⁷ T m
    • C. 40π × 10⁻⁷ T m
    • D. 16π × 10⁻⁷ T m
  24. Q29. Two long straight parallel wires 10 cm apart carry 3 A each in opposite directions. The magnetic field at the point midway between them is:

    • A. 4.8 × 10⁻⁵ T
    • B. zero
    • C. 1.2 × 10⁻⁵ T
    • D. 2.4 × 10⁻⁵ T
  25. Q30. A galvanometer of resistance 99 Ω is to be converted into an ammeter that reads 100 times its full-scale current. The required shunt resistance is:

    • A. 1 Ω
    • B. 0.01 Ω
    • C. 0.99 Ω
    • D. 99 Ω