An electric field is a field quantity defined as the force received by a charge divided by the amount of charge placed there. It is treated as a vector field.
Basic Knowledge
Electric field E [N/C = V/m] is defined as:E = F / q (the force F acting on a test charge q divided by q)
The electric field produced by a point charge Q at distance r is E = kQ/r²; its direction is outward for positive Q and inward for negative Q.
Electric field lines:
・Curves that leave positive charges and enter negative charges
・The tangent drawn to an electric field line gives the direction of the electric field
・The number of lines per unit area indicates the magnitude of the electric field (electric flux density)
・They do not intersect or end midway
Principle of superposition: The electric field produced by multiple charges is the vector sum of the fields produced by each charge.E_total = E₁ + E₂ + ...
Electric field E (electric field) (Force acting on a unit charge. Unit: N/C = V/m)
Electric field line (electric field line) (An imaginary line representing the direction and strength of an electric field)
Principle of superposition (Electric fields and potentials are found by vector and scalar addition, respectively)
Uniform electric field (An electric field with constant magnitude and direction, such as inside a parallel-plate capacitor)
Gauss’s law (The total number of electric field lines passing through a closed surface is proportional to the charge inside)
Further Study (Background and Significance)
The electric field is the origin of Faraday’s concept of a “field.” It provides a physical picture of local action (transmission through a field), rather than action at a distance. The completion of electromagnetism (Maxwell’s equations) also arose from this field-based viewpoint.
Gauss’s law: the number of electric field lines passing through a closed surface = total charge inside / ε₀. In problems with symmetry (spheres, cylinders, or planes), it greatly simplifies integral calculations.
The motion of a charge in a uniform electric field is treated like uniformly accelerated motion and frequently appears in calculations of charged-particle trajectories.
- E = F/q (has direction: a vector)
- Electric field produced by point charge Q: E = kQ/r²
- Electric field lines: positive→negative, never intersecting
- Electric field-line density ∝ electric-field strength
- Superposition: E_total = ΣE_i (vector sum)
- Uniform electric field: charged particles undergo uniformly accelerated motion
- Gauss’s law makes calculations for symmetric fields easier
Points to Note (Easily Confused)
① E is a vector. Distinguish its magnitude from its direction. ② The number of electric field lines has only relative meaning (the absolute number has no meaning). ③ A point where E = 0 does not necessarily have V = 0, and the converse is also true. ④ Superposition is vector addition, so calculate each component when the charges are not on the same straight line.
Practice
- State the magnitude and direction of the electric field at a point a distance r from a point charge +Q.
- Equal and opposite charges +Q and −Q are placed on the x-axis at x = +a and x = −a. Find the direction and magnitude of the electric field at the origin O.
- Explain why electric field lines cannot intersect.