22-Elec-A7 Electromagnetics
Worked solutions to 14 past sittings (2013–2019), 113 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.
- Characteristic Impedance (2 sittings): May 2018 Q7 · May 2013 Q7
- Standing-wave ratio (2 sittings): May 2016 Q2 · December 2013 Q2
Questions by sitting
December 2019
- Question 1: Standing-wave measurement on a mismatched line
- Question 2: Oblique incidence at a lucite–air interface
- Question 3: Step transient on a doubly mismatched line
- Question 4: WR-90 rectangular waveguide at 10 GHz
- Question 5: Faraday induction in a circular loop
- Question 6: Parallel-plate capacitor and displacement current
- Question 7: Charged conducting sphere
December 2018
- Question 1: Pulse echoes from two shunt taps on an endless line
- Question 2: Placing the protective stubs of a two-band diplexer
- Question 3: The two lowest propagating modes at 15 GHz and their velocities
- Question 4: Vertical component of H in an obliquely climbing plane wave
- Question 5: Terminal voltage of a rod crossing a slab of magnetic field
- Question 6: Electric field and power density of a circularly polarised wave
- Question 7: Penetration depth of a 10 GHz wave into mercury
- Question 8: Scaling a short-element field in frequency, range and angle
May 2018
- Question 1: Energy in the Reflected Pulse, and the Highest Non-Overlapping Repetition Rate
- Question 2: The Two Lowest Frequencies for a Short-Circuited Stub Across a Matched Load
- Question 3: EMF Induced in a Bar Rotating in a Vertical Field
- Question 4: RMS Vertical Component of E in an Obliquely Travelling Wave
- Question 5: Behaviour Beyond a Dielectric-to-Air Step in a Rectangular Waveguide
- Question 6: Magnetic Field Above a Circulating Electron
- Question 7: Characteristic Impedance and Velocity of a Two-Layer Coaxial Line
- Question 8: Where the Radiation Field Overtakes the Biot–Savart Field
December 2017
- Question 1: Steady-state terminal-voltage pattern of a pulsed line with a shunt tap
- Question 2: Length of a short-circuited stub that matches at 300 MHz and isolates the load at 600 MHz
- Question 3: Spacing and amplitude of the circularly polarised planes formed by two crossed beams
- Question 4: Cut-off frequencies of the three lowest modes of a dielectric-filled rectangular waveguide
- Question 5: Rms EMF induced in a loop by an obliquely arriving plane wave
- Question 6: Horizontal magnetic field above a semicircular loop fed by two infinite straight wires
- Question 7: Self-inductance of two stacked solenoids for like and opposed senses of circulation
- Question 8: Where two quadrature current elements radiate a linearly polarised field
May 2017
- Question 1: Pulse reflections from two matched shunt taps on an infinite line
- Question 2: Which branch receives which frequency — a stub diplexer
- Question 3: Distributed parameters of a two-ribbon strip line
- Question 4: Filling permittivity that places the dominant cut-off at 4.2 GHz
- Question 5: Vertical component of E in a wave climbing at 45 degrees
- Question 6: Field at the centre of two orthogonal semicircles
- Question 7: EMF induced in a loop crossing a wall of field
- Question 8: Short vertical element radiating at two frequencies
December 2016
- Question 1: Pulse Train on a Mismatched Transmission Line
- Question 2: Parallel Open- and Short-Circuited Line Sections
- Question 3: Characteristic Impedance of a Two-Layer Coaxial Line
- Question 4: Polarisation of Two Crossed Plane Waves
- Question 5: Rotating Direction-Finding Loop in the Earth’s Field
- Question 6: Two Lowest Resonances of a Rectangular Cavity
- Question 7: Torque on a Current Loop in a Uniform Field
- Question 8: Power Density Radiated by a Short Horizontal Element
May 2016
- Question 1: Step response of a line feeding two semi-infinite lines
- Question 2: Standing-wave ratio and the real-impedance point
- Question 3: Polarisation of two counter-propagating orthogonal waves
- Question 4: Shortest and longest guide wavelength at 20 GHz
- Question 5: Inductance and stored energy of a partly cored solenoid
- Question 6: Line parameters of a parallel-ribbon line
- Question 7: Propagation velocity and loss of a lossy line
- Question 8: Magnetic field of a short vertical radiator off the horizontal plane
December 2015
- Question 1: Pulse energy delivered to two parallel semi-infinite lines
- Question 2: Shorted stub that passes 300 MHz and blocks 400 MHz
- Question 3: Coaxial line: inner conductor diameter and dielectric constant
- Question 4: Mode count in a 2.5 cm × 1 cm guide at 20 GHz
- Question 5: Power limit set by the standing-wave voltage maximum
- Question 6: Power reflected at normal incidence on a dielectric
- Question 7: Interference of two crossed plane waves
- Question 8: Vertical field component from a short element at a new frequency
May 2015
- Question 1: Step response of an open-circuited line with a shunt tap
- Question 2: Open-circuited stub matching a parallel RC load
- Question 3: Rotating loop in an inclined field: best axis and rms EMF
- Question 4: Loop current for a specified field at a jumper centre
- Question 5: Single-mode bandwidth of an empty rectangular waveguide
- Question 6: Quarter-wave line: generator EMF variation with load power
- Question 7: Counter-propagating orthogonal waves: distance to circular polarisation
- Question 8: Vertical elements over a ground plane: the 30 MHz vertical field
December 2014
- Question 1: Pulse energy split at a junction of two semi-infinite lines
- Question 2: Section length giving a purely resistive input impedance
- Question 3: Circular polarisation from two counter-propagating waves
- Question 4: Power limit set by the voltage ceiling on a mismatched line
- Question 5: Propagating modes and longest guide wavelength at 15 GHz
- Question 6: Self-inductance of a solenoid with a partial magnetic core
- Question 7: Mechanical power to drive a loop generating into a complex load
- Question 8: Magnetic field of a monopole above a conducting ground plane
May 2014
- Question 1: Pulse Echoes from Two Shunt Taps on an Infinite Line
- Question 2: A Load Shunted by a Matched Pair of Open and Shorted Stubs
- Question 3: Sizing a 50 Ω Coaxial Line
- Question 4: Power Coupled into Seawater at 1 GHz
- Question 5: Guide Wavelength, and What Happens When the Dielectric Is Removed
- Question 6: Reading a Plane Wave from a Loop Probe
- Question 7: Scaling a Short Monopole's Field to a New Frequency and a New Direction
- Question 8: A Vertical Electrostatic Dipole above a Conducting Plane
December 2013
- Question 1: Pulse Train on a Doubly Mismatched Line
- Question 2: Stub-Loaded Termination and Standing-Wave Ratio
- Question 3: EMF Induced in a Rotating Pick-Up Loop
- Question 4: Single-Mode Band of a Dielectric-Filled Waveguide
- Question 5: Circular Polarization from Two Crossed Current Elements
- Question 6: Displacement Current from the Circulation of H
- Question 7: Plane-Wave Attenuation in Seawater
- Question 8: Evanescent Field above a Totally Reflecting Water Surface
May 2013
- Question 1: Step Response of an Infinite Line with a Shunt Resistor
- Question 2: Stub and Quarter-Wave Matching Network at 300 MHz
- Question 3: Rotating Loop — Load Power and RMS Torque
- Question 4: Attenuation of a Below-Cutoff Rectangular Waveguide
- Question 5: Surface Current Induced by Oblique Incidence on a Conducting Plane
- Question 6: Power Capability of a Voltage-Limited Line
- Question 7: Characteristic Impedance and Velocity of a Ribbon Line
- Question 8: Short Radiating Element Moved onto a Conducting Plane
Undated paper
- Question 1: Oblique incidence at a free-space / silica interface
- Question 2: Standing-wave pattern on a mismatched 50 Ω line
- Question 3: Step transient on a doubly mismatched 75 Ω line
- Question 4: A road tunnel as a rectangular waveguide
- Question 5: Field and potential of a radially graded charge cloud
- Question 6: Resistance, current density and dissipation in a cylindrical resistor
- Question 7: Line charge and point charge by Gauss' law and superposition
- Question 8: Ampère's law for a wire with graded current density
- Question 9: On-axis field and self-flux of a circular current loop
- Question 10: Radiation resistance, efficiency and far field of a short vertical antenna