NUMS — Medical & Dental Entry Test

NUMS Physics — Electricity and Magnetism (Set 5)

Take the NUMS Physics — Electricity and Magnetism (Set 5): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer review. Covers…

What this test covers

• 30 NUMS Physics

Sample questions with answers

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

1. Q1. Charges +4.0 µC and +1.0 µC are fixed 30 cm apart in air. At what point on the line between them is the net electric field zero?

   • A. 24 cm from the +4.0 µC charge
   • B. 20 cm from the +4.0 µC charge ✓
   • C. 10 cm from the +4.0 µC charge
   • D. 15 cm from the +4.0 µC charge

   Answer: B. 20 cm from the +4.0 µC charge

   Explanation: Set kq₁/x² = kq₂/(0.30 − x)²: 4/x² = 1/(0.30 − x)², so 2(0.30 − x) = x, x = 0.20 m from the larger charge.

2. Q2. An electric dipole of moment 2.0 × 10⁻⁹ C m is placed in a uniform field of 5.0 × 10³ N C⁻¹ at 30° to the field. What is the torque on it?

   • A. 2.5 × 10⁻⁶ N m
   • B. 1.0 × 10⁻⁵ N m
   • C. 8.7 × 10⁻⁶ N m
   • D. 5.0 × 10⁻⁶ N m ✓

   Answer: D. 5.0 × 10⁻⁶ N m

   Explanation: τ = pE sinθ = 2.0 × 10⁻⁹ × 5.0 × 10³ × sin 30° = 1.0 × 10⁻⁵ × 0.5 = 5.0 × 10⁻⁶ N m.

3. Q3. Four identical charges of +2.0 nC are placed at the corners of a square of side 0.20 m. What is the electric potential at the centre of the square, taking V = 0 at infinity? (k = 9.0 × 10⁹ N m² C⁻²)

   • A. 254 V
   • B. 509 V ✓
   • C. 1020 V
   • D. 360 V

   Answer: B. 509 V

   Explanation: Each corner is a/√2 = 0.141 m from the centre. V = 4kq/r = 4 × 9.0 × 10⁹ × 2.0 × 10⁻⁹/0.1414 = 509 V (potentials add as scalars).

4. Q4. An alpha particle (charge +2e, mass 6.64 × 10⁻²⁷ kg) is accelerated from rest through a potential difference of 1000 V. What is its final speed? (e = 1.60 × 10⁻¹⁹ C)

   • A. 6.2 × 10⁵ m s⁻¹
   • B. 3.1 × 10⁵ m s⁻¹ ✓
   • C. 2.2 × 10⁵ m s⁻¹
   • D. 1.0 × 10⁷ m s⁻¹

   Answer: B. 3.1 × 10⁵ m s⁻¹

   Explanation: ½mv² = qV = 2 × 1.60 × 10⁻¹⁹ × 1000 = 3.2 × 10⁻¹⁶ J. v = √(2 × 3.2 × 10⁻¹⁶/6.64 × 10⁻²⁷) = 3.1 × 10⁵ m s⁻¹.

5. Q5. A solid conducting sphere of radius 10 cm carries a charge of 20 nC. Taking V = 0 at infinity (k = 9.0 × 10⁹ N m² C⁻²), what is the potential at its centre?

   • A. 18 000 V
   • B. 180 V
   • C. 1800 V ✓
   • D. 0 V

   Answer: C. 1800 V

   Explanation: Charge resides on the surface and the interior is an equipotential. V at the centre = V at the surface = kq/R = 9.0 × 10⁹ × 20 × 10⁻⁹/0.10 = 1800 V, although the field there is zero.

The other 25 questions

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6. Q6. A 4.0 µF capacitor is charged to 100 V and then connected in parallel to an uncharged 6.0 µF capacitor. How much energy is lost in the process?

   • A. 12 mJ
   • B. 0 mJ
   • C. 20 mJ
   • D. 8.0 mJ

7. Q7. In an electrolytic cell, 5.0 × 10¹⁸ Na⁺ ions cross a plane to the right and 3.0 × 10¹⁸ Cl⁻ ions cross the same plane to the left in 2.0 s (each ion carries a charge of magnitude e = 1.60 × 10⁻¹⁹ C). What is the current through the plane?

   • A. 0.64 A
   • B. 0.32 A
   • C. 0.16 A
   • D. 1.28 A

8. Q8. A 60 W, 220 V bulb and a 100 W, 220 V bulb are connected in series across a 220 V supply. What power does the 60 W bulb dissipate? (Assume the filament resistances stay at their rated values.)

   • A. 23.4 W
   • B. 14.1 W
   • C. 60 W
   • D. 37.5 W

9. Q9. A battery of emf 12 V and internal resistance 2.0 Ω is connected to a variable load. What is the maximum power that can be delivered to the load?

   • A. 12 W
   • B. 72 W
   • C. 18 W
   • D. 36 W

10. Q10. A thin metal strip 0.10 mm thick carries a current of 5.0 A in a perpendicular magnetic field of 0.50 T. The metal has 8.5 × 10²⁸ free electrons per m³ (e = 1.60 × 10⁻¹⁹ C). Using V_H = IB/(n t e), what is the Hall voltage across the strip?

    • A. 1.8 × 10⁻³ V
    • B. 4.6 × 10⁻⁷ V
    • C. 3.7 × 10⁻⁶ V
    • D. 1.8 × 10⁻⁶ V

11. Q11. In a velocity selector, a uniform electric field of 2.0 × 10⁴ V m⁻¹ is perpendicular to a magnetic field of 0.010 T. Charged particles of what speed pass through undeflected?

    • A. 2.0 × 10⁸ m s⁻¹
    • B. 5.0 × 10⁻⁷ m s⁻¹
    • C. 2.0 × 10⁶ m s⁻¹
    • D. 2.0 × 10² m s⁻¹

12. Q12. A proton (m = 1.67 × 10⁻²⁷ kg, e = 1.60 × 10⁻¹⁹ C) circulates in a cyclotron in a uniform magnetic field of 1.5 T. What is the cyclotron frequency?

    • A. 143 MHz
    • B. 45.8 MHz
    • C. 3.6 MHz
    • D. 22.9 MHz

13. Q13. A proton enters a uniform magnetic field of 0.10 T with speed 2.0 × 10⁶ m s⁻¹ at 60° to the field direction. What is the pitch of its helical path? (m = 1.67 × 10⁻²⁷ kg, e = 1.60 × 10⁻¹⁹ C)

    • A. 0.33 m
    • B. 1.1 m
    • C. 0.66 m
    • D. 0.038 m

14. Q14. Two long parallel wires 20 cm apart carry equal currents of 5.0 A in opposite directions. What is the magnetic field midway between them? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)

    • A. 2.0 × 10⁻⁵ T
    • B. 1.0 × 10⁻⁵ T
    • C. 4.0 × 10⁻⁵ T
    • D. 0

15. Q15. A toroid with 500 turns has a mean radius of 10 cm and carries a current of 2.0 A. What is the magnetic field inside the core (air)? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)

    • A. 1.3 × 10⁻² T
    • B. 6.3 × 10⁻⁴ T
    • C. 2.0 × 10⁻⁵ T
    • D. 2.0 × 10⁻³ T

16. Q16. A coil of 200 turns and resistance 10 Ω is connected to a galvanometer of negligible resistance. The magnetic flux through each turn changes by 5.0 × 10⁻³ Wb. How much charge flows through the coil?

    • A. 0.10 C
    • B. 1.0 × 10⁻³ C
    • C. 0.50 C
    • D. 20 C

17. Q17. A metal rod of length 0.50 m rotates uniformly about one end in a plane perpendicular to a uniform magnetic field of 0.20 T, at an angular speed of 40 rad s⁻¹. What emf is induced between its ends? (emf = ½Bωl²)

    • A. 2.0 V
    • B. 0.50 V
    • C. 4.0 V
    • D. 1.0 V

18. Q18. A long air-cored solenoid has 1000 turns, length 0.50 m and cross-sectional area 2.0 × 10⁻⁴ m². What is its self-inductance? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)

    • A. 3.1 × 10⁻³ H
    • B. 5.0 × 10⁻⁴ H
    • C. 2.5 × 10⁻⁷ H
    • D. 1.3 × 10⁻³ H

19. Q19. A series circuit with a 30 Ω resistor and a pure inductor of reactance 40 Ω is connected to a 100 V (r.m.s.) AC supply. What average power is dissipated?

    • A. 120 W
    • B. 200 W
    • C. 333 W
    • D. 160 W

20. Q20. An LC circuit has L = 10 mH and C = 0.40 µF. What is its natural oscillation frequency?

    • A. 0.40 kHz
    • B. 16 kHz
    • C. 2.5 kHz
    • D. 6.3 kHz

21. Q21. An ideal-turns-ratio step-down transformer converts 2200 V to 220 V and supplies a 10 A load on the secondary. Its efficiency is 90%. What current does the primary draw?

    • A. 1.00 A
    • B. 0.90 A
    • C. 1.11 A
    • D. 10 A

22. Q22. A parallel-plate capacitor is charged and then disconnected from the battery. A dielectric slab of constant K = 4 completely fills the gap. By what factor does the stored energy change?

    • A. It decreases to ¼ of its original value
    • B. It decreases to ½ of its original value
    • C. It increases fourfold
    • D. It is unchanged

23. Q23. Four identical cells, each of emf 1.5 V and internal resistance 1.0 Ω, are connected to an external resistance of 0.25 Ω. Which arrangement gives the largest current, and what is it?

    • A. All four in parallel; 6.0 A
    • B. All four in parallel; 3.0 A
    • C. All four in series; 1.4 A
    • D. Two series pairs in parallel; 2.4 A

24. Q24. A 2.0 kW electric heater runs for 3.0 hours every day for 30 days. If a unit (1 kWh) costs Rs 40, what is the cost of the electricity used?

    • A. Rs 14 400
    • B. Rs 720
    • C. Rs 2400
    • D. Rs 7200

25. Q25. Why is a lightning conductor made with a sharply pointed tip?

    • A. A pointed tip has more surface area to absorb the lightning strike
    • B. A pointed tip attracts opposite charge by a magnetic force from the cloud
    • C. Charge density and field are greatest at sharp points, so charge leaks away
    • D. A sharp tip has lower resistance, so current flows through it more easily

26. Q26. In a Millikan-type experiment, an oil drop of radius 1.00 µm and density 900 kg m⁻³ is held stationary by a vertical electric field of 1.15 × 10⁵ V m⁻¹ (g = 9.8 m s⁻²; e = 1.60 × 10⁻¹⁹ C). How many elementary charges does the drop carry?

    • A. 1
    • B. 4
    • C. 3
    • D. 2

27. Q27. A wire bent into a semicircle of radius 0.10 m carries a current of 5.0 A. What is the magnetic field at the centre of the semicircle? (μ₀ = 4π × 10⁻⁷ T m A⁻¹; B = μ₀I/4R for a semicircular arc)

    • A. 6.3 × 10⁻⁵ T
    • B. 1.6 × 10⁻⁵ T
    • C. 7.9 × 10⁻⁶ T
    • D. 3.1 × 10⁻⁵ T

28. Q28. In the Bohr model an electron orbits the hydrogen nucleus with frequency 6.58 × 10¹⁵ Hz in the ground state. What is the equivalent circulating current? (e = 1.60 × 10⁻¹⁹ C)

    • A. 1.05 µA
    • B. 1.05 A
    • C. 1.05 mA
    • D. 0.105 mA

29. Q29. A 10 V battery of negligible internal resistance is connected across two 100 kΩ resistors in series. A voltmeter of resistance 100 kΩ is connected across one of the resistors. What does it read?

    • A. 5.0 V
    • B. 10 V
    • C. 3.3 V
    • D. 6.7 V

30. Q30. Air breaks down in an electric field of about 3.0 × 10⁶ V m⁻¹. What is the largest potential difference that can be applied across two parallel plates 2.0 mm apart in air before sparking occurs (ignoring edge effects)?

    • A. 6.0 × 10³ V
    • B. 1.5 × 10³ V
    • C. 6.0 × 10⁶ V
    • D. 1.5 × 10⁹ V