Electric Field of Discrete Charges
For point sources, E(r) = sum_i k q_i (r-r_i)/|r-r_i|^3. The field direction is the force direction on a positive test charge.
Why this shows up in the exam
Field at a square corner · Field at a circle centre · Finding charge ratios from field direction
Learn the idea
Electric field is force per positive test charge and superposes as a vector. A source configuration sets a field at a point even before a test charge is placed there. Symmetry and components usually simplify the vector sum.
🧠 Memory hook: Pretend the test charge is positive, then add field arrows.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E = F/q₀ — definition in the test-charge limit
- E = sum_i k q_i R_i/R_i³ — vector field of discrete point charges
How to approach it
- 1Draw source-to-field-point vectors
- 2Resolve and sum field components
- 3Check units N/C and symmetry
Common slip-ups that cost marks
- •Multiplying by a test charge when only E is asked
- •Adding scalar field magnitudes
- •Reversing the field of a negative source
🌟 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.