Electric Field Lines
Electric field lines are discontinuous curves. They start from a positively charged body and end at a negatively charged body. Bo electric lines of force exist inside the charged body. Thus electrostatic field lines do not form any closed loops.
Note 1: if there is a single charge, the electric filed lines may start or end at infinity. For example due to a single positive charge, field lines would start from the charge and end at infinity. Due to a single negative charge, field lines would start from infinity and end at the negative charge.
Note 2: we shall study in unit 3 that magnetic lines of force are continuous (or endless) as against the electric lines of force which are discontinuous.
Tangent to the electric field line at any point gives the direction of electric intensity al that point.
No two electric lines of force can intersect eachother. This is because at the point of intersection p, we can draw two tangents PA ad PB to the two lines of force,
This would mean two directions of electric intensity at the same point which is not possible hence no two lines of force can cross each other.
The electric filed lines are always normal to the surface of a conductor either while starting or ending on the conductor. Therefore there is no component of electric field intensity parallel to the surface of the conductor.
The electric field lines contract longitudinally on account of attraction between unlike charges.
The electric field lines exert a lateral pressure on account of repulsion between like charges.
Note. For pictorial representation of E due to a point change at the origin we draw vectors pointing along the direction of electric field the lengths of vectors are proportional to the strength of the field at each point As E ∝ (1 / r2) therefore the vectors get shorter as one goes away from the charge. Shoes such a picture when we connect the arrows pointing in one direction, the resulting figure represents a field line. We thus obtain many field lines, all pointing radically outwards from the point charge.
The magnitude of the field is represented by the density of field lines, near the charge lines are closer, so the density of field lines is more and hence electric field E is strong neat the charge. Always from the charge the field lines are well separated the density of field lines is smaller and hence electric field E is weaker ways from the charge. We may therefore, define electric intensity at a point as equal to number of field lines crossing normally a unit area around that point.
As field lines are three dimensional and all figures are drawn on the plane of the paper (in two dimensions) therefore to estimate the density of field lines we have to consider the number of field lines per unit cross-sectional area perpendicular to the lines. We know that in three dimensions the solid angle Δ Ω subtended by a small perpendicular plane area Δ S at a distance r can be written as Δ Ω = Δ S / r2 we know that with a charge q at the apex o of the cone number of radial field lines in a given solid angle is the same. In let us consider two points P1 and P2 at distances r1 and r2 respectively from the charge.
At P1, area subtended by the solid angle Δ Ω is r12 Δ Ω . At p2 area subtended by the solid angle Δ Ω is r22× Δ Ω .
The number of field lines cutting these area elements are the same let it be n.
∴ Number of field lines cutting unit Ares element at p1 = electric intensity at p1 E1 = (n/ r12) Δ Ω , and number of field lines cutting unit area element at p2 = electric intensity at p2 E2 = n / r22 Δ Ω
Clearly; E1 / E2 = {[r22 / r12] E ∝ (1 / 2)}
Electric field intensity is more near the charge and vice-versa.
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