Flux for Charges on Boundaries
Join identical solids around the boundary location, apply total flux q/epsilon_0 to the assembled closed surface, then divide by symmetry among copies and requested faces.
Why this shows up in the exam
Charge at a cube face centre · Charge at a corner or edge · Cuboid opposite-face flux
Learn the idea
A charge on a corner, edge, or face is handled by assembling copies so the charge becomes internal to a symmetric closed surface. A boundary point charge makes the field singular, so a naive enclosed-charge count is ambiguous. Symmetric replication gives the intended limiting flux assignment.
🧠 Memory hook: Move a boundary charge inside by building mirror copies.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Phi_assembled = q/epsilon₀ — Gauss flux after symmetric assembly
- Phi_piece = Phi_assembled/N — share for N equivalent replicated solids
How to approach it
- 1Identify face, edge, or corner placement
- 2Assemble the minimal symmetric solid
- 3Apply Gauss and divide by proven equivalence
Common slip-ups that cost marks
- •Calling a boundary charge fully enclosed without a limiting convention
- •Dividing by eight for every boundary position
- •Assuming all original faces are equivalent
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Two point charges 1 microC and 2 microC are 1 m apart in vacuum. Take k = 9 x 10^9 SI. Find the force magnitude.
More from Electrostatics
Electric dipoles and molecular dipole moments
Study the properties of electric dipoles, their fields and potentials, behavior in electric fields, and the distinction between polar and non-polar molecules.
Capacitors, capacitance, and combinations
Learn about parallel plate capacitors, series and parallel combinations, and how capacitance changes with geometry and dielectrics.
Energy stored in capacitors and conservation of charge
Examine how energy is stored, transferred, or lost in capacitors, including during charging, discharging, and redistribution, and the principle of charge conservation.
Gauss's law and its applications
Learn Gauss's law, electric flux, and how to use symmetry to find electric fields of charged spheres, shells, and other symmetric objects.
Coulomb's law and electric field of point charges
Understand Coulomb's law, the principle of superposition, and how to calculate the electric field due to point charges and simple charge distributions.
Conductors, charge distribution, and electrostatic shielding
Understand how charges distribute on conductors, the concept of electrostatic shielding, and the minimization of potential energy in conductors.