Electric Lines of Force

Just as wind flow can be visualised using streamlines, an invisible electric field can be visualised using electric lines of force. This concept converts an abstract, three-dimensional vector field into an intuitive picture that helps in solving both theoretical and numerical problems quickly.

Electric line of force is an imaginary curve drawn in an electric field such that the tangent at any point on it gives the direction of the electric field at that point.

• It represents the path along which a unit positive test charge would tend to move if free to do so.
• Lines are imaginary — they have no physical existence; they are a visualization tool only.

1. Isolated Positive Charge: This diagram shows the electric field originating from a single, isolated positive charge. The field lines are directed radially outward, reflecting the repulsive nature of the charge.

2. Isolated Negative Charge: In contrast to the positive charge, this diagram shows the electric field lines for an isolated negative charge. The lines are directed radially inward, indicating the direction a positive test charge would be pulled.

3. Electric Dipole: This diagram visualizes the field created by two equal and opposite charges. The field lines are curved, starting on the positive charge (+q) and terminating on the negative charge (−q). The field is densest in the region directly between the two charges.

4. Two Equal Like Charges (Positive): This diagram illustrates the repulsion between two identical positive charges. The field lines diverge outward from both charges, and they bend away from each other, indicating a repulsive force. A "neutral point," where the net electric field is zero, exists exactly at the midpoint between them.

5. Charged Conducting Plate: This diagram shows a large, flat, charged conducting plate. Since the plate is a conductor, the charge distributes itself uniformly (on both surfaces, though only one is fully visible here). The resulting electric field lines are perpendicular to the surface of the plate and are uniformly spaced, indicating a constant electric field strength near the surface.

6. Parallel Plate Capacitor: This final diagram visualises the most uniform practical electric field: a parallel plate capacitor. It consists of two large, closely spaced conducting plates carrying equal and opposite charges. In the central region between the plates, the electric field lines are parallel and equally spaced, representing a nearly uniform field. Near the edges of the plates, the field lines curve outward, a phenomenon known as "fringing."

Setup

The example uses three sets of electric field line diagrams to test how the number and density of field lines reveal charge sign, relative magnitude, and field strength at specific points.

(i) Sign and ratio of two charges

Since field lines start on positive charges and end on negative charges, q₂ (source of 18 lines) is positive and q₁ (receiving 6 lines) is negative. The ratio is found using the line cne count: \[\begin{vmatrix} \frac{q_1}{q_2} \end{vmatrix}=\frac{N_1}{N_2}=\frac{6}{18}=\frac{1}{3}\], meaning ∣q₂∣ = 3∣q₁∣ - q₂ is three times stronger than q₁.

(ii) Equal charges and field strength at three points

Both charges are positive and equal in magnitude, since each emits the same number of lines (N = 18). Point A sits where lines are denser, so the field there is stronger than at point B, where lines are more spread out. Point C has no lines passing through it at all, meaning the two fields exactly cancel there — the resultant field is zero.shaalaa

(iii) Three charges, solving for q₁ and q₃

Lines start at q₁ and q₃ and end at q₂, so q₁ and q₃ are positive while q₂ is negative. Using the the line-count ratio: \[\begin{vmatrix} \frac{q_1}{q_2} \end{vmatrix}=\frac{8}{16}=\frac{1}{2}= \begin{vmatrix} \frac{q_3}{q_2} \end{vmatrix}\], so q₁ and q₃ are each half the magnitude of q₂. Given q₂ = –20 nC, this gives q₁ = q₃ = +10 nC.

Key takeaway

This example demonstrates the core principle that field-line count is proportional to charge magnitude, letting you compare or calculate unknown charges purely from a diagram, while line density at a point indicates local field strength (dense = strong, absent = zero).

Electric field lines behave like wind streamlines or water flow lines — you cannot see the wind or the field directly, but the lines show you the direction and relative strength of the flow at every point in space.