Electric Field and Applications of Electrostatics
Senior 2 · Physics
Electric Field and Applications of Electrostatics
Lesson 2 of 5
22 min
Real objects rarely carry just one charge. A thundercloud has positive charge at the top and negative charge at the bottom; the drum of a photocopier carries a pattern of charge shaped like the page being copied. To predict what happens, you need two skills: drawing the field of several charges, and adding the fields or forces from each charge. This lesson gives you both.
Just as for magnets, we draw an electric field with field lines. The rules are:
| Arrangement | Pattern |
|---|---|
| Isolated positive point charge | Straight lines pointing radially outward, like the spokes of a wheel |
| Isolated negative point charge | Straight lines pointing radially inward |
| Equal positive and negative charges (a dipole) | Lines leave the + charge and curve round to enter the − charge; the field is strongest between them |
| Two equal positive charges | Lines from each charge bend away from the other; midway between them there is a neutral point where the field is zero |
| Two parallel plates with opposite charges | Straight, parallel, evenly spaced lines from the + plate to the − plate: a uniform field (except near the edges) |
When several charges act on one point, each produces its own field or force as if the others were not there. The total is the vector sum. In this unit the charges lie on one straight line, so the vectors are all parallel: choose one direction as positive (say, to the right), give each force or field a sign, and add.
Worked example 1: forces. Three charges lie on a line. A (+3.0 μC) is 0.10 m to the left of C (+1.0 μC), and B (−2.0 μC) is 0.20 m to the right of C. Find the resultant force on C. (k = 9.0 × 10⁹ N·m²/C²)
Worked example 2: fields. Charges of +4.0 nC and +1.0 nC are 0.20 m apart. Find the field at the midpoint, 0.10 m from each.
Between two like charges there is a point where their fields are equal and opposite. For +4.0 μC and +1.0 μC placed 0.30 m apart, let the neutral point be x metres from the +4.0 μC charge. The fields are equal when
k(4.0)/x² = k(1.0)/(0.30 − x)². Taking square roots: 2/x = 1/(0.30 − x), so 0.60 − 2x = x, giving x = 0.20 m.
The neutral point is 0.20 m from the larger charge and 0.10 m from the smaller one: always closer to the smaller charge.
In Charges and Fields, place two positive charges a few grid squares apart, tick Electric Field, and look for the point between them where the arrows vanish: the neutral point. Now stack four positive charges on one spot and one on another, and see the neutral point move towards the single charge.
Tip
Superposition in three steps: (1) choose a positive direction; (2) work out the SIZE of each field or force separately with kQ/r²; (3) decide each DIRECTION from "away from +, towards −" (or "like repel, unlike attract" for forces), give it a sign, and add.
Never put the signs of the charges into kQ/r² and hope the direction comes out right: find directions with a sketch.
Take k = 9.0 × 10⁹ N·m²/C².
Sketch the field of two equal positive charges and mark the neutral point.
Solution: Lines leave each charge radially and bend away from the other charge; none join the two. The neutral point is exactly midway between them.
Charges of +2.0 nC and −2.0 nC are 0.20 m apart. Find the field at the midpoint.
Solution: Each gives E = 9.0 × 10⁹ × 2.0 × 10⁻⁹ ÷ 0.10² = 1800 N/C. The field of the + charge points away from it (towards the − charge); the field of the − charge points towards itself (also towards the − charge). Same direction, so add: 3600 N/C towards the negative charge.
Charges of +9.0 μC and +1.0 μC are 0.40 m apart. Where is the neutral point?
Solution: 9/x² = 1/(0.40 − x)², so 3/x = 1/(0.40 − x), giving 1.2 − 3x = x and x = 0.30 m from the +9.0 μC charge (0.10 m from the smaller one).
Why can there be no neutral point between a positive and a negative charge?
Solution: Between them, the field of the + charge points away from it (towards the − charge) and the field of the − charge also points towards the − charge. The two fields point the same way, so they add and can never cancel there.
Remember
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