Q.Explain why two lines of force in an electric field cannot intersect each other.
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Properties of Electric Field Lines
What Are Electric Field Lines?
Imagine you're standing in a field of invisible forces. Every positive charge pushes other positive charges away, and every negative charge pulls them in. If you could release a tiny positive test charge anywhere in space, it would instantly feel a push in some direction — that direction is the electric field at that point.
Now, if you let that test charge move freely, it would trace out a path through space. That path is an electric field line. It's not a real physical line — it's a visual tool, like contour lines on a map, that shows you which way the electric force points at every location.
Field lines are not trajectories of a moving charge (unless the charge starts from rest and no other forces act). They show the direction of force at each point, not the path a charge will take.
The Four Rules, Built from Intuition
1. Field lines start on positive charges and end on negative charges
Think of a positive charge as a source that "emits" field lines outward in all directions. A negative charge is a sink — lines "drain" into it. If you have a single isolated positive charge, its field lines radiate outward to infinity. A single negative charge has lines coming in from infinity.
Why? Because the electric field points away from a positive charge (repelling a test positive charge) and toward a negative charge (attracting it). The line simply follows that direction from start to finish.
2. Field lines never intersect
At any point in space, the electric field has one unique direction. If two field lines crossed, that point would have two different directions for the field — which is impossible. The field can't point both left and right at the same spot.
A common mistake: thinking field lines can "touch" or "meet" at a charge. They don't — they begin or end there, but they don't cross each other even at the charge's location.
3. The density of field lines tells you the field strength
Where field lines are packed closely together, the electric field is strong. Where they are spread far apart, the field is weak. This is a visual convention: we draw more lines per unit area in regions of stronger field.
For a point charge, lines spread out as you move away — the same number of lines passes through larger and larger spheres, so the density drops as 1/r2, exactly matching Coulomb's law.
4. Field lines are perpendicular to the surface of a conductor
When you place a conductor in an electric field, charges inside rearrange until the field inside becomes zero. At the surface, the field must be perpendicular — if it had a component parallel to the surface, charges would keep moving along the surface. So field lines always meet a conductor's surface at a right angle.
Putting It All Together …
A field line is drawn tangent to the field direction at each point, so a crossing point would carry two tangents at once; since the field there is the single unique vector sum of all sources, two directions are impossible. …
If two lines of force intersected, the electric field at the point of intersection would have two directions simultaneously, which contradicts the fact that the field at a given point is single-valued.
An electric line of force is drawn such that the tangent to it at any point gives the direction of the electric field E at that point. Suppose two field lines did cross at a point P. Then at P we could draw two different tangents — one for each line — implying two different directions for E at the same point simultaneously.
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- CBSE 2024Set ANNUAL1 markMCQQ.The angle between equipotential surface and electric line of force at a point is(a) 0°(b) 45°(c) 90°(d) 180°
›Reveal solutionSolution
Equipotential surfaces and electric field lines always meet at right angles.
An equipotential surface is a surface on which the electric potential V has the same value at every point. If the electric field E had any component along the equipotential surface, moving a test charge along that surface would require work (since W = qE·dl along that component), and the potential would change — contradicting the definition of an equipotential surface.
Therefore the electric field (and hence the electric line of force, which is tangent to E at every point) can have no component along the surface; the field must be directed entirely along the normal to the surface. This means:
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- CBSE 2024Set ANNUAL1 markQ.The field lines of a single positive charge are radially __________.
›Reveal solutionSolution
Field lines of an isolated positive charge point away from it in every direction, since the force on a small positive test charge is repulsive (away from the source charge).
Electric field lines show the direction a positive test charge would move if placed at that point. For an isolated positive point charge, the force on a nearby positive test charge is repulsive, pushing it directly away from the charge along the line joining them.
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- CBSE 2023Set F1 markMCQQ.Electric field lines provide information about (A) field strength (B) direction (C) nature of charge (D) all of these
›Reveal solutionSolution
Electric field lines convey direction (tangent), strength (density of lines), and the nature of charge (start on +, end on −).
An electric field line carries several pieces of information:
- Direction: the tangent at any point gives the direction of E there.
- Field strength: where lines are crowded (dense) the field is strong, and where they are sparse it is weak. …
- CBSE 2023Set ANNUAL1 markQ.Show the electric field lines due to a single positive charge (q > 0).
›Reveal solutionSolution
For a single isolated positive point charge, the electric field lines are straight lines pointing radially outward from the charge in every direction, uniformly spread in 3-D (spherically symmetric).
Since E=4πε01r2qr^ for a point charge, the field vector at every point in space is directed along the radius vector away from the charge (for q>0). So the field-line diagram is: the charge q sits at the centre, and an evenly-spaced set of straight lines emerge from it and extend outward to infinity in all directions - denser near the charge (stronger field) and spreading apar …
- CBSE 2023Set ANNUAL1 markQ.State true or false: Two field lines never intersect.
›Reveal solutionSolution
True. If two field lines intersected, the field at that point would have two different directions, which is impossible since the field at any point is unique.
Electric field lines represent the direction of the electric field at every point in space — the tangent to a field line at any point gives the direction of E there.
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- CBSE 2022Set GC1 markQ.Electric field lines do not intersect each other. Explain.
›Reveal solutionSolution
A field line's tangent gives the direction of E. Two crossing lines would give two directions at one point, which is impossible — so they cannot intersect.
The tangent to an electric field line at any point gives the direction of the electric field there. If two lines intersected, we could draw two tangents at the point of intersection, implying the electric field points in two directions at once. Since the electric field at a point can have only **on …
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