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Grade 10-11 (age 15-17)

high school physics Electric Field and Electric Potential

An electric field is the property of the space around a charge that lets it exert a force on other charges. Just as there is a magnetic field around a magnet, there is an electric field around a charge. Another charge placed in an electric field feels a force, and the field strength is defined as the force on +1 C placed at that point. The field strength falls off with the square of the distance and the potential with the distance itself, and equipotential surfaces, which join points of equal potential, always cross the field lines at right angles. Move the charge slider and the number and direction of the field lines and the field strengths at 2 m and 4 m change; the distance slider shows as a bar how the attraction between two charges shrinks with the square of the distance.

What an Electric Field Is

⚡ An invisible region of force
①Just as there is a magnetic field around a magnet, there is an electric field around a charge
②Another charge placed in the field feels a force
③The field strength E is the size of the force on +1 C placed at that point
④The electric field is a vector with a direction, while the potential is a scalar with size only

Field Lines and Equipotential Surfaces

3 μC
💡 Rules for field lines
①Field lines leave positive charges and enter negative charges
②The denser the field lines, the stronger the field
③Field lines never cross one another
④Equipotential surfaces always meet field lines at right angles
⑤At twice the distance the same number of lines spreads over a sphere 4 times larger, so E becomes 1/4

Coulomb's Law and the Electric Field

5
Coulomb's law
F = kQ₁Q₂r²
k = 9 × 10⁹ N·m²/C². Like signs repel and unlike signs attract
Field strength
E = kQr² [N/C = V/m]
The field at distance r from a point charge Q
📐 Key relations
①A charge in an electric field feels the force F = qE
②Doubling the distance between two charges makes the force 1/4
③Fields from several charges add as vectors
④The bar in the figure shows the force as (2/r)² times the force at distance 2

Potential and the Electric Field

Electric potential
V = kQr [V]
The work needed to bring +1 C from infinitely far away to distance r
Field and potential difference
E = -ΔVΔr
The field is the rate of change of potential with distance, pointing toward lower potential
🏔️ Comparing with terrain
①Potential is like height: a positive charge moves from higher potential to lower
②The field is like the slope: the faster the potential changes, the stronger the field
③Equipotential surfaces are like contour lines: moving along one, the electric force does no work
④Around a positive charge the potential is higher closer in; around a negative charge it is lower closer in

Worked Examples

Example 1
Where the electric field strength is 200 N/C, a charge of +0.5 C is placed. What electric force does it feel?
1
A charge in an electric field feels the force F = qE.
F = qE
2
Put in q = 0.5 C and E = 200 N/C.
F = 0.5 × 200 = 100 N
▸ 100 N
A positive charge is pushed along the field, and a negative charge against it.
Example 2
Parallel plates 0.02 m apart have 100 V across them. What is the strength of the uniform field between them?
1
The uniform field between parallel plates is E = V/d.
E = Vd
2
Put in V = 100 V and d = 0.02 m.
E = 1000.02 = 5000 V/m
▸ 5000 V/m (= 5000 N/C)
Between parallel plates the field is the same everywhere, E = V/d; V/m and N/C are the same unit.

Summary

Electric field
E = kQr²
in N/C
Potential
V = kQr
in V (volts)
CSAT-style problem, adapted
If the distance from a point charge doubles, how does the field strength at that point change?
①Doubles
②Halves
③Quadruples
④Becomes one quarter
⑤Stays the same
▸ ④ Becomes one quarter
1
The field of a point charge is E = kQ/r², inversely proportional to the square of the distance.
E = kQr2
2
If r doubles, r² becomes 4 times larger, so E becomes 1/4.
r→2r ⇒ E ∝ 1(2r)2 = 14E
🎯 Exam Points
①In Coulomb's law F = kQ₁Q₂/r², like signs repel and unlike signs attract
②The field E = kQ/r² is a vector that falls off with the square of the distance
③The potential V = kQ/r is a scalar that falls off with the distance
④Moving along an equipotential surface, the electric force does no work
⑤The field points in the direction of decreasing potential
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Current and Resistance

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