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QPage 119: Q7: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Page 119: Q7 Solution: In some old texts it is mentioned that lines of force originate …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often read "4\pi lines of force" as a literal number of lines, but field lines are a visual aid, not discrete objects. The factor 4\pi comes from the surface area of a unit sphere in Gauss’s law, so the statement merely reflects the geometry of flux, not an integer count of lines.

In some old texts it is mentioned that 4π4\pi lines of force originate from each unit positive charge. Comment on the statement in view of the fact that 4π4\pi is not an integer.

Step-by-Step Verified Solution

**Answer:** The statement is a simplified way of describing the field, not a literal count of lines. **Step-by-Step Explanation:** The number "4�" arises from the geometry of a sphere: the surface area of a unit sphere is 4�. It is not an integer because the electric field is a continuous quantity, and field lines are a visual aid. The actual number of field lines is arbitrary (depending on how many lines you choose to draw per unit charge). The statement means that the flux through a unit sphere around a unit charge is 1/ϵ01/\epsilon_0, which involves 4� in the derivation. It is not meant to be a literal count .

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