Chapter 23: Coulomb’s law Chapter outline ■ ■ ■ ■ ■ ■
understand that the charge on a spherical conductor may be considered to act as a point charge at its centre recall and use Coulomb’s law to solve problems recall and use the formula for the field strength of a point charge define the electric potential at a point and use the equation for the potential of a point charge relate field strength and potential due to a point charge compare electric fields and gravitational fields
KEY TERMS
Coulomb’s law: any two point charges exert an electrical force on each other that is proportional to the product of their charges and inversely proportional to the square of the distance between them the electric potential at a point: the work done in bringing a unit positive charge from infinity to that point kQ Q 1 Equations: Coulomb’s law: F = 1 2 where k = r2 4 πε 0 electric potential =
work done W ;V= charge Q
kQ 1 electric potential: V = where k = r 4 πε 0 field strength = potential gradient; gradient E =
ΔV Δd
Exercise 23.1 Electric field around a point charge You have already studied general ideas about electric fields (Chapter 8). You have also studied gravitational fields (Chapter 18). This exercise extends these ideas to consider electric fields around point electric charges. Note: permittivity of free space, ε0 = 8.85 × 10 −12 F m−1. 1 This question revises the idea of an electric field. a State what is meant by an electric field. b Write the equation that defines electric field strength. Give the equation in words and also in symbols. State the unit of each quantity in the equation. This diagram shows an electron placed in an electric field of strength 5000 N C−1: electric field electron
Earth
The electron is close to the Earth’s surface where the gravitational field strength g = 9.81 N kg−1.
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