04-BS-9
Worked solutions to 14 past sittings (2013–2019), 110 questions. Pick a sitting, or start from a topic below.
- December 2019
- December 2018
- May 2018
- December 2017
- May 2017
- December 2016
- May 2016
- December 2015
- May 2015
- December 2014
- May 2014
- December 2013
- May 2013
- Undated paper
Topics across the sittings
Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.
- Capacitance (3 sittings): December 2019 Q6 · May 2014 Q2 · December 2013 Q5
Questions by sitting
December 2019
- Question 1: Electric Field and Force from Two Point Charges
- Question 2: Charge Distribution and Field of a Charged Conducting Spherical Shell
- Question 3: Magnetic Field of a Cylindrical Current-Carrying Pipe
- Question 4: Magnetic Field and Force Near a Finite-Width Current Sheet
- Question 5: EMF Induced in a Rotating and in a Stationary Rectangular Loop
- Question 6: Capacitance, Charge, Energy and Force of a Silicon-Filled Parallel-Plate Capacitor
- Question 7: Magnetomotive Force, Flux and Inductances of a Gapped Two-Winding Magnetic Core
December 2018
- Question 1: Capacitance of a Parallel-Plate Capacitor with Graded Permittivity
- Question 2: Inductance of a Solenoid with a Half-Inserted Magnetic Core
- Question 3: Magnetic Flux Density from a Finite-Thickness Sub-Surface Current Layer
- Question 4: Minimum Midpoint Charge to Cancel Mutual Repulsion of Two Point Charges
- Question 5: Motional EMF Induced in a Moving Rod Crossing a Vertical Field
- Question 6: Reflection and Refraction of a Plane Wave at an Air–Water Interface
- Question 7: Magnetic Flux Density at the Center of a Three-Quarter-Circle Current Loop
- Question 8: Velocity Selector — Magnetic Field Cancelling an Electric Deflecting Force
May 2018
- Question 1: Field Discontinuity Across a Sphere's Thin Surface-Charge Layer
- Question 2: Total Electrostatic Energy of a Charge Triangle with Protons at the Centroid
- Question 3: Magnetic Flux Density at the Surface of an Accelerated Electron Beam
- Question 4: Magnetic Flux Density at the Midpoint and at the Jumper Centres of a Long Rectangular Current Loop
- Question 5: Current Density Producing a Triangular H(x) Profile
- Question 6: EMF Induced in a Square Loop Crossing a Finite-Width Vertical Field Region
- Question 7: Maximum Stored Energy in a Parallel-Plate Capacitor with a Partial Dielectric Layer
- Question 8: Horizontal Offset Between the Apparent and Real Position of an Insect Seen From Underwater
December 2017
- Question 1: Electric Field on an Electron in a Triangle of Electrons with Protons at the Centre
- Question 2: Electric Field at the Surface of a Uniformly Charged Electron Beam
- Question 3: Maximum Stored Energy in a Coaxial Line at the Dielectric Breakdown Limit
- Question 4: Force Between Two Antiparallel Current-Carrying Wires
- Question 5: EMF Induced in a Moving Loop Crossing a Spatially Varying Field
- Question 6: On-Axis Field of a Clockwise Current Loop, 1 m Above the Centre
- Question 7: Charge Distribution Producing a Linear-in- r Field That Vanishes Outside a Sphere
- Question 8: Time Interval Between a Directly Reflected and a Refracted-and-Reflected Light Beam
May 2017
- Question 1: Field Jump Across a Charged Surface Layer Covering a Uniformly Charged Sphere
- Question 2: Magnetic Field Between Three Coaxial Current-Carrying Cylinders
- Question 3: On-Axis Field of a Clockwise Current Loop
- Question 4: RMS EMF of a Coil Rotating About a Vertical Diameter in a Tilted Field
- Question 5: Minimum Plate Area for a Dielectric-Filled Capacitor at the Breakdown Limit
- Question 6: Mutual Inductance of Two Coaxial Solenoids
- Question 7: Charge Density Distribution That Produces a Given Quadratic Field Inside a Slab
- Question 8: Apparent vs. Actual Location of an Underwater Mirror Viewed Obliquely
December 2016
- Question 1: Field Inside a Point Charge Embedded in a Uniformly Charged Sphere
- Question 2: Electric Potential Above a Charged Equilateral Triangle
- Question 3: Minimum Plate Area for a Capacitor at the Air Breakdown Limit
- Question 4: Magnetic Flux Density of a Finite-Radius Straight Conductor
- Question 5: On-Axis Field of an Atomic-Scale Current Loop
- Question 6: Motional EMF of a Rod Moving Through a Tilted Magnetic Field
- Question 7: Electric Field on the Equatorial Plane of a Dipole Potential
- Question 8: Tilt Angle of a Ground Mirror Reflecting Light Between Two Towers
May 2016
- Question 1: Electric Field of a Point-Charge Dipole Off-Axis
- Question 2: Stored Energy in a Circular Parallel-Plate Capacitor
- Question 3: Magnetic Flux Density Midway Between Two Parallel Current Loops
- Question 4: RMS EMF of a Loop Rotating in a Uniform DC Magnetic Field
- Question 5: Charge Distribution Producing a Given Piecewise Radial Field
- Question 6: Magnetic Field Keeping an Injected Electron on a Straight Path
- Question 7: Power Distribution in a DC Generator, Line, and Load
- Question 8: Apparent Displacement of a Submerged Object Viewed Obliquely
December 2015
- Question 1: Electric Field Above a Charged Ring with a Central Point Charge
- Question 2: Electric Field Between Two Nested Uniformly-Charged Spheres
- Question 3: Minimum Capacitor Plate Radius for a Target Stored Energy
- Question 4: Magnetic Field Cancelling an Electric Force on a Moving Electron
- Question 5: Magnetic Flux Density at the Centre of a Bent Semicircular Loop
- Question 6: Magnetic Fields Around a Three-Conductor Coaxial Transmission Line
- Question 7: Induced Voltage Across a Gapped Loop in a Collapsing Field
- Question 8: Time Delay Between Skywave and Ground-Wave Arrivals
May 2015
- Question 1: Electric Field on a Corner Electron of a Charged Square
- Question 2: Electric Field at the Surface of a Charged Electron Beam
- Question 3: On-Axis B Field of a Horizontal Current Loop
- Question 4: B Field Between Two Antiparallel Current Sheets
- Question 5: Maximum and Minimum EMF of a Shrinking Loop
- Question 6: Electric Field in a Capacitor from Stored Energy
- Question 7: Mutual Inductance of Two Coaxial Loops of Very Different Size
- Question 8: Mirror Location and Time Delay for a Reflected Light Pulse
December 2014
- Question 1: H Field at the Centre of a Bent Semicircular Loop
- Question 2: Field Inside a Point Charge Surrounded by a Uniform Charge Sphere
- Question 3: Capacitance of a Coaxial Transmission Line
- Question 4: Mutual Inductance of Two Concentric Loops at an Angle
- Question 5: RMS EMF of a Loop Rotating About a Tilted Horizontal Diameter
- Question 6: H Field Amplitude of a Plane EM Wave
- Question 7: Self-Energy of a Uniformly Charged Spherical Surface
- Question 8: Time-Average Torque on a Synchronously Rotating AC Loop
May 2014
- Question 1: E Field and Potential Between Two Charged Layers
- Question 2: Coaxial Capacitor — Capacitance and Breakdown Voltage
- Question 3: B Field at the Midpoint of a DC Transmission Line
- Question 4: B Field at the Centre of a Bent Semicircular Loop
- Question 5: RMS EMF Induced in a Loop by an Oscillating Horizontal Field
- Question 6: Solenoid Inductance With a Partial Magnetic Slug
- Question 7: Electrostatic Energy of a Point Charge and Four Corner Charges
- Question 8: Velocity-Selector Capacitor Voltage for a Moving Electron
December 2013
- Question 1: Potential Inside a Point-Charge-Plus-Layer Distribution
- Question 2: On-Axis B Field of a Finite Cylindrical Current Layer
- Question 3: H Field Between Two Antiparallel Infinite Current Sheets
- Question 4: RMS EMF of a Loop Rotating in a Uniform Field
- Question 5: Circular Capacitor — Capacitance and Breakdown-Limited Energy
- Question 6: Inductance of a Solenoid on a Cored Winding
- Question 7: E Field of a Plane Wave from Maxwell's Equations
- Question 8: Power Delivered and Power Lost — Two Parallel Transmission Lines
May 2013
- Question 1: Concentric Spherical Capacitor — Breakdown-Limited Charge
- Question 2: Magnetic Field of a Circular Current Loop
- Question 3: RMS EMF Induced by a Rotating Uniform Field
- Question 4: Torque on a Current Loop in a Uniform Field
- Question 5: Displacement Current in a Parallel-Plate Capacitor
- Question 6: Electric Field of a Point-Charge Pair (Dipole)
- Question 7: Transmission-Line Efficiency Comparison
- Question 8: Radar Pulse Delay Through Air and Water
Undated paper
- Question 1: Two Point Charges — Field, Cancelling Charge, Force and Work
- Question 2: Point Charges Enclosed by a Charged Conducting Shell
- Question 3: Magnetic Field of a Solid Cylindrical Conductor
- Question 4: Right-Angle Bent Conductor — Field and Self-Force
- Question 5: EMF Induced in a Rectangular Loop — Rotational and Transformer Cases
- Question 6: Parallel-Plate Capacitor and a Levitated Charged Sphere
- Question 7: Magnetic Circuit — Gapped Core with Two Windings