NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Electricity and Magnetism (Set 6): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer review. Covers…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A point charge q is placed at one corner of a cube. What is the total electric flux through the whole surface of the cube?
Answer: B. q/(8ε₀)
Explanation: Eight identical cubes sharing that corner would enclose the charge completely, so each receives 1/8 of the total flux q/ε₀. The flux through this cube is q/(8ε₀) (it is zero through the three faces that meet at the charge and q/24ε₀ through each of the other three).
Q2. For a short electric dipole, how do the magnitudes of the field at a distance r along its axis and at the same distance r on its equatorial (perpendicular bisector) line compare?
Answer: A. The axial field is twice the equatorial field
Explanation: For a short dipole E_axial = 2kp/r³ and E_equatorial = kp/r³, so the axial field is twice as large.
Q3. Charges +q, +q, −q and −q are placed at the four corners of a square in that order going round it, so the two positive charges are adjacent. What is the situation at the centre of the square?
Answer: B. The potential is zero but the electric field is not zero
Explanation: The potentials of the four equal-distance charges cancel (+q, +q, −q, −q), so V = 0. The fields of the two positive charges point away from them and those of the negative charges point towards them; both pairs add in the direction from the + side to the − side, so E ≠ 0.
Q4. A 4 μF capacitor charged to 100 V and a 6 μF capacitor charged to 50 V are connected, with the positive plate of each joined to the negative plate of the other. What is the common potential difference after connection?
Answer: C. 10 V
Explanation: Charges: Q₁ = 4 × 100 = 400 μC and Q₂ = 6 × 50 = 300 μC. Joined with opposite polarity, the net charge is 400 − 300 = 100 μC on 10 μF in parallel, so V = 100/10 = 10 V. (Same-polarity connection would give 70 V.)
Q5. A parallel-plate capacitor is connected to a battery and the battery stays connected. A dielectric slab (K = 3) is then inserted so that it completely fills the space between the plates. By what factor does the stored energy change?
Answer: A. Increases by a factor of 3
Explanation: With the battery connected, V is fixed. C increases by K = 3, so U = ½CV² increases by a factor of 3, and the battery supplies the extra charge. (If the battery were disconnected, U would fall by a factor of 3.)
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Q6. A galvanometer of resistance 50 Ω gives full-scale deflection for a current of 2.0 mA. What series resistance converts it into a voltmeter reading up to 10 V?
Q7. A battery has emf 12 V and internal resistance 3.0 Ω. What is the maximum power it can deliver to an external resistor of adjustable resistance?
Q8. A 12 V battery of negligible internal resistance is connected to a 4 Ω resistor in series with a parallel pair of 6 Ω and 3 Ω resistors. What current flows through the 3 Ω resistor?
Q9. A uniform wire of resistance 12 Ω is cut into three equal pieces, and the three pieces are then connected in parallel. What is the resistance of the combination?
Q10. Two identical small balls of mass 0.10 kg, each carrying the same charge, hang from a common point on light insulating threads 0.50 m long. They come to rest 0.60 m apart. Taking g = 10 m s⁻² and k = 9.0 × 10⁹ N m² C⁻², what is the charge on each ball?
Q11. An electron moving horizontally at 2.0 × 10⁷ m s⁻¹ enters the uniform field of 1000 V m⁻¹ between two horizontal plates, each 5.0 cm long. Ignoring gravity, how far has it been deflected on leaving the plates? (e = 1.60 × 10⁻¹⁹ C, mₑ = 9.11 × 10⁻³¹ kg)
Q12. What is the energy stored per unit volume in an electric field of 3.0 × 10⁵ V m⁻¹ in air? (ε₀ = 8.85 × 10⁻¹² F m⁻¹)
Q13. Five identical 6.0 Ω resistors are connected in a Wheatstone-bridge arrangement: four form the arms and the fifth is the bridge between the two middle junctions. What is the equivalent resistance between the two opposite corners where the battery is connected?
Q14. A cyclotron has a magnetic field of 1.5 T and accelerates protons (m = 1.67 × 10⁻²⁷ kg, e = 1.60 × 10⁻¹⁹ C). What is the frequency of the alternating voltage applied to its dees?
Q15. Singly charged ³⁵Cl⁻ and ³⁷Cl⁻ ions are accelerated through the same potential difference and enter a uniform magnetic field perpendicular to their path, which bends them through semicircles. The ³⁵Cl⁻ ions follow a path of radius 0.200 m. How far apart on the detector do the two isotopes land? (Take the ion masses as proportional to 35 and 37.)
Q16. Two long straight parallel wires 0.20 m apart carry currents of 5.0 A and 3.0 A in opposite directions. What is the magnitude of the magnetic field at the midpoint between them? (μ₀/4π = 10⁻⁷ T m A⁻¹)
Q17. A long solenoid of length 0.25 m has 500 turns and carries a current of 2.0 A. What is the magnetic field at the centre of its axis? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)
Q18. A bar magnet of magnetic moment 0.50 A m² lies in a uniform field of 0.20 T, aligned with it (stable equilibrium). How much work is needed to rotate it through 180° so that it points against the field?
Q19. A coil of 50 turns and area 0.020 m² is placed with its plane perpendicular to a uniform field of 0.40 T, and is connected to a circuit of total resistance 10 Ω. It is quickly turned through 180°. What total charge flows through the circuit?
Q20. A strong magnet is dropped down a vertical copper tube. Why does it take much longer to emerge than a non-magnetic piece of the same shape and mass?
Q21. A 12 V battery is connected at t = 0 to a coil of inductance 0.50 H and resistance 10 Ω (the resistance of the whole circuit). What is the current at t = 0.050 s?
Q22. A 100 Ω resistor is connected in series with an ideal inductor whose reactance is 100 Ω, across a 200 V rms, 50 Hz supply. What is the average power dissipated in the circuit?
Q23. A half-wave rectifier passes only the positive half-cycles of a sinusoidal current of peak value 10 A. What is the rms value of the resulting current?
Q24. A plane electromagnetic wave in vacuum has an electric-field amplitude of 100 V m⁻¹. What is its average intensity? (ε₀ = 8.85 × 10⁻¹² F m⁻¹, c = 3.0 × 10⁸ m s⁻¹)
Q25. A straight wire 0.50 m long carries 4.0 A in a uniform magnetic field of 0.30 T. The wire makes an angle of 30° with the field. What is the magnitude of the force on the wire?
Q26. A conducting rod of length 0.40 m slides at a constant 5.0 m s⁻¹ on frictionless rails in a perpendicular field of 0.50 T. The circuit has a total resistance of 2.0 Ω. What external force is needed to keep it moving at constant speed?
Q27. The magnetic susceptibility of a paramagnetic salt obeys Curie's law, χ ∝ 1/T. If its temperature is raised from 300 K to 600 K, by what factor does the susceptibility change?
Q28. Why is it relatively safe to stay inside a closed metal car during a lightning storm?
Q29. A rectangular current-carrying loop is placed in a uniform magnetic field with its plane parallel to the field lines. Which statement is correct?
Q30. An LC circuit has L = 2.0 mH and C = 50 µF. The capacitor initially holds a charge of 100 µC and the resistance is negligible. What is the maximum current in the inductor?