ECAT — Engineering College Admission Test (UET)
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
The first 5 questions of this test, with the correct answer and explanation.
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:
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.
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:
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.
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:
Answer: C. 2π × 10⁻⁴ T
Explanation: B = μ₀NI/2r = (4π×10⁻⁷)(20)(2.5)/(2 × 0.05) = 2π × 10⁻⁴ T.
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:
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.
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:
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.
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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:
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:
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:
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:
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:
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:
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:
Q13. A strong bar magnet is dropped vertically down the axis of a long vertical copper tube. Compared with free fall, the magnet falls:
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:
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:
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:
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:
Q18. An alternating current has a peak value of 10 A. Its mean (average) value over one half cycle is approximately:
Q19. A heater of resistance 5 Ω carries a sinusoidal alternating current of peak value 4 A. The average power dissipated is:
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:
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:
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:
Q23. A pure inductor is connected to an AC source. The average power absorbed by the inductor over a complete cycle is:
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:
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:
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:
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:
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:
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:
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: