Q.What is the ratio of the charges q1/q2 for the following electric field line pattern (the number of field lines emerging from each charge is proportional to its magnitude)?
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.
Note
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.
Watch out
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
Consider two equal positive charges placed a distance apart. The field lines bulge outward from each charge, and in the region exactly midway between them, the fields from both charges cancel — the field is zero there. No line passes through that point. The lines curve away from the midpoint, never crossing, and eventually go to infinity.
For a positive and a negative charge (a dipole), lines start on the positive, curve smoothly through space, and end on the negative. The densest crowding occurs near the charges themselves, where the field is strongest.
Number of lines per unit area ∝∣E∣
Why These Rules Matter
These properties let you sketch the electric field for any charge distribution without doing a single calculation. You can see where the field is strong, where it's zero, and how charges interact — all from a simple drawing. In exams, these rules are the foundation for solving problems on field patterns, conductors, and equilibrium of charges.
The key insight: field lines are not real, but they obey real physics. Every rule follows directly from the definition of the electric field itself.
Properties of electric field lines are introduced early in the NCERT Class 12 Physics Electrostatics chapter, and 'properties of electric field lines class 12 physics' or 'electric field lines important questions' are common searches among students revising for boards. These four rules are also the basis for several JEE Main and NEET conceptual questions on field patterns around conductors and dipoles.
The number of field lines emerging from a charge is proportional to its magnitude.
✓Final answer
(d) 2511
Step 1. The density (and total count) of field lines drawn emerging from a point charge in a field-line diagram is, by construction, taken proportional to the magnitude of that charge -- more field lines are drawn leaving a larger charge.
Step 2. Counting the field lines shown emerging from q1 against those emerging from q2 in the given pattern gives the two charges in the ratio 11:25.
Step 3. Therefore q1/q2=11/25, matching option (d), and none of the other listed ratios (1/5, 25/11, 5) match the line count shown.
✓Final answer
(d) 2511
Count the field lines emerging from each charge in the figure; their ratio equals the ratio of the charge magnitudes.
Inverting the ratio (reading it as q2/q1 instead of q1/q2).
Assuming field-line count relates to charge by an inverse-square rule rather than direct proportionality -- it is a direct, linear proportionality by convention.