Q.Show the electric field lines due to a single positive charge (q > 0).

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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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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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. …

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 $\vec E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}\hat r$ 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 …

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 $\vec{E}$ there.

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A field line's tangent gives the direction of $\vec E$. 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 …