Problem — Reading a graph: field of a dipole

Problem

Reading a graph: field of a dipole. Sketch qualitatively the electric field lines of a dipole formed by $+q$ and $-q$ at distance $d$. Discuss the curvature of the lines, their density and their physical meaning.

Solution

Origin and direction of the lines. Field lines leave the positive charge $+q$ and terminate at the negative charge $-q$: their direction indicates that of the force on a positive test charge.

Curvature. The lines are curved: they leave $+q$ radially, curve, and re-enter $-q$ radially. The curvature reflects the superposition of the two fields $\vv{E} = \vv{E}_+ + \vv{E}_-$; only along the axis joining the charges does a line remain straight.

Density and physical meaning. Where the lines are denser the field is stronger; where they are sparser it is weaker. The density is greatest near the charges (strong field) and decreases with distance, where the lines thin out. In general, the density of field lines is proportional to $\abs{\vv{E}}$.

$\ev{\text{Linee da } +q \text{ a } -q;\ \text{curve; dense (E forte) vicino alle cariche, rade (E debole) lontano}}$

Linked atoms

Topics: Campo elettrico e potenziale Concepts: Dipolo elettrico · Campo elettrico Skills: Lettura dei grafici