NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Electricity and Magnetism (Set 4): 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. Charges +4q and +q are fixed 30 cm apart. At what distance from the +4q charge, on the line between them, is the net electric field zero?
Answer: A. 20 cm
Explanation: Fields cancel when 4q/x² = q/(0.30 − x)². So 2/x = 1/(0.30 − x), giving x = 20 cm from the +4q charge (the neutral point is nearer the weaker charge).
Q2. A large uniformly charged non-conducting sheet carries a surface charge density of 2.0 μC m⁻². What is the electric field near it? (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²)
Answer: D. 1.13 × 10⁵ N C⁻¹
Explanation: E = σ/(2ε₀) = 2.0 × 10⁻⁶/(2 × 8.85 × 10⁻¹²) = 1.13e+05 N C⁻¹, independent of distance.
Q3. A solid non-conducting sphere of radius 20 cm carries a uniformly distributed charge of 8.0 μC. What is the electric field at 10 cm from its centre? (1/4πε₀ = 9 × 10⁹ N m² C⁻²)
Answer: C. 9.0 × 10⁵ N C⁻¹
Explanation: Inside a uniform sphere the enclosed charge is Q(r/R)³, so E = kQr/R³ = 9 × 10⁹ × 8 × 10⁻⁶ × 0.10/(0.20)³ = 9.0e+05 N C⁻¹. Using the point-charge formula would give 7.2 × 10⁶.
Q4. A charge of +2.0 μC is moved from 1.0 m to 0.50 m from a fixed charge of +5.0 μC. How much work is done by the external agent? (1/4πε₀ = 9 × 10⁹ N m² C⁻²)
Answer: A. 0.09 J
Explanation: W = kQq(1/r₂ − 1/r₁) = 9 × 10⁹ × 5 × 10⁻⁶ × 2 × 10⁻⁶ × (2 − 1) = 0.09 J (positive: moving closer against repulsion).
Q5. Three charges of +1.0 μC each are placed at the corners of an equilateral triangle of side 10 cm. What is the electric potential energy of the system? (1/4πε₀ = 9 × 10⁹ N m² C⁻²)
Answer: D. 0.27 J
Explanation: There are three pairs, each with U = kq²/a = 9 × 10⁹ × 10⁻¹²/0.1 = 0.09 J. Total = 0.27 J.
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Q6. A parallel-plate capacitor has plate separation 5.0 mm. A dielectric slab of constant 3 and thickness 3.0 mm is inserted, leaving an air gap, between the plates. By what factor does the capacitance change?
Q7. A 4.0 μF capacitor charged to 100 V is connected, plates +/+ and −/−, to an uncharged 6.0 μF capacitor. How much energy is lost?
Q8. A parallel-plate capacitor is charged and disconnected from the battery. A dielectric slab of constant 4 is then inserted to fill the gap. How does the stored energy change?
Q9. A 5.0 μF capacitor discharges through a 2.0 MΩ resistor. How long does it take for the charge to fall to half its initial value? (ln 2 = 0.693)
Q10. A copper wire of cross-section 1.0 mm² carries 2.0 A. If copper has 8.5 × 10²⁸ free electrons per m³, what is the electron drift speed? (e = 1.6 × 10⁻¹⁹ C)
Q11. A wire of resistance 10 Ω is drawn uniformly (constant volume) to three times its original length. What is its new resistance?
Q12. A 60 W bulb and a 100 W bulb, both rated for 220 V, are connected in series across a 220 V supply. What power does the 100 W bulb dissipate (assuming constant resistances)?
Q13. The heating coil of an electric heater is cut so that its length is reduced by 20%, and it is connected to the same supply voltage. By what percentage does the power dissipated increase?
Q14. Cells (12 V, 1 Ω) and (6 V, 2 Ω) are connected in parallel (like poles together) across a 4 Ω resistor. What current flows through the 4 Ω resistor?
Q15. In a potentiometer the balance length for a cell of emf E is 60 cm on open circuit and 50 cm when the cell is closed through a 9.0 Ω resistor. What is the internal resistance of the cell?
Q16. In a meter bridge, a 6.0 Ω resistor is in the left gap and an unknown resistor X in the right gap. The balance point is 40 cm from the left end. What is X?
Q17. Two long parallel wires 10 cm apart carry currents of 10 A and 20 A in the same direction. What is the force per metre of length between them? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)
Q18. A circular coil of 50 turns and radius 10 cm carries 2.0 A. What is the magnetic field at its centre? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)
Q19. A toroid has 1000 turns and carries 2.0 A. What is the magnetic field inside its core at a mean radius of 20 cm? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)
Q20. A proton and an alpha particle (mass 4 u, charge +2e) enter the same uniform magnetic field perpendicular to it with the same kinetic energy. What is the ratio of the radii of their circular paths, r(α) : r(p)?
Q21. A coil of 100 turns, area 0.020 m² and current 0.50 A sits in a uniform field of 0.20 T with its magnetic moment along the field. How much work is needed to turn it through 180°?
Q22. A coil of 100 turns and area 0.020 m² rotates at 50 revolutions per second in a uniform field of 0.10 T. What is the peak emf generated?
Q23. An inductor of 0.50 H is connected in series with a 10 Ω resistor and a 20 V battery. What is the current one time constant after the switch is closed?
Q24. A series circuit has R = 30 Ω, inductive reactance 60 Ω and capacitive reactance 20 Ω across a 220 V (rms) supply. What is the average power dissipated?
Q25. What is the resonant frequency of a series circuit with L = 0.10 H and C = 10 μF?
Q26. A step-down transformer converts 2200 V to 220 V and delivers 2200 W to a load at 90% efficiency. What current flows in the primary?
Q27. 100 kW of power is sent along a line of resistance 5.0 Ω at 2.0 kV. What is the power lost in the line?
Q28. An electromagnetic wave in vacuum has a peak electric field of 300 V m⁻¹. What is its average intensity? (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻², c = 3.0 × 10⁸ m s⁻¹)
Q29. A 1.0 kW immersion heater is 80% efficient. How long does it take to warm 2.0 kg of water by 50 K? (specific heat of water 4200 J kg⁻¹ K⁻¹)
Q30. A wire carrying 5.0 A is bent into a semicircle of radius 10 cm. What is the magnetic field at the centre of the semicircle due to the arc? (μ₀ = 4π × 10⁻⁷ T m A⁻¹)