Questions: Electric Field and Coulomb's Law

Question 1

A source charge Q = +4 μC is fixed in space. A test charge q = +2 μC is placed 0.3 m away. What does the electric field E at that location represent?

• A. The total electrostatic force on the test charge q
• B. The force per unit positive test charge — a property of that point in space, independent of q
• C. The potential energy stored between Q and q
• D. The force multiplied by the distance between Q and q

Answer: (B)

The electric field E at a point is defined as the force per unit positive test charge: E = F/q. It is a property of that location in space due to the source charges, independent of whatever test charge you place there. The actual force on a specific charge q is F = qE. Confusing 'field' with 'force on a specific charge' misses the key abstraction: the field exists everywhere in space whether or not a test charge is present, and tells you what force any charge placed there would experience.

Question 2

Two electric field lines are drawn crossing at a point in a diagram. What does this indicate?

• A. The field is especially strong at that point
• B. A charge must be located precisely at the crossing point
• C. This is impossible — field lines never cross because the field has only one direction at each point
• D. The two field lines originated from charges of opposite sign

Answer: (C)

Electric field lines never cross because the electric field has a unique direction at every point in space. If two lines crossed, the field at that intersection would have two directions simultaneously — a physical contradiction. The field direction at any point is determined by the vector sum of contributions from all source charges (superposition), which always yields exactly one resultant vector. Crossing field lines indicate an error in the drawing, not a real phenomenon.

Question 3

The electric field at a point in space exists primarily when a test charge is physically present there to experience it.

• T. True
• F. False

Answer: False

The electric field is a property of space itself, created by source charges, and exists at every point regardless of whether a test charge is present. This is the key conceptual shift in field theory: instead of treating interactions as direct action-at-a-distance between charges, the source charge creates a field throughout space, and any charge placed in that field experiences a force. The field is real — it carries energy and momentum — not just a bookkeeping device. This becomes essential later when fields propagate as electromagnetic waves, entirely independent of the charges that created them.

Question 4

The electric potential at a point and the electric field at that point both measure the same physical quantity, expressed in different units.

• T. True
• F. False

Answer: False

Electric field E is force per unit charge (N/C, equivalently V/m). Electric potential V is potential energy per unit charge (volts = J/C). They are related — E = −∇V — but they are fundamentally different quantities. The field is a vector (direction matters); the potential is a scalar. Confusing them is one of the most common errors in introductory electromagnetism. A region can have a nonzero potential but zero field (e.g., inside a conductor at equilibrium), and vice versa. Keeping force and energy clearly distinct is the prerequisite for understanding both.

Question 5

Why is the concept of the electric field — rather than simply applying Coulomb's law between pairs of charges — essential for describing electromagnetic phenomena?

Model answer: Coulomb's law only describes the force between two isolated point charges. The electric field concept enables superposition: the total field at any point equals the vector sum of contributions from every source charge, turning multi-charge problems into tractable calculations. For continuous charge distributions, this sum becomes a vector integral. More fundamentally, the field is an entity that exists independently of test charges, carries energy, and propagates at the speed of light as an electromagnetic wave. The field picture is the correct framework for radiation, relativity, and ultimately quantum electrodynamics — none of which can be described by direct action-at-a-distance.

The 'action-at-a-distance' picture (charge A directly pushes charge B) works for static point charges but breaks down when charges accelerate and when fields propagate through vacuum. The field is the intermediary that makes the causal chain local: the source creates the field, the field travels through space, and the field acts on the test charge. This locality is what makes the theory compatible with special relativity.