Page 379 - Physics Coursebook 2015 (A level)

Chapter 23: Coulomb’s law
Gravitational fields
Electric fields
Origin
arise from masses
Vector forces
only gravitational attraction, no repulsion
Units
F in N, g in N kg−1 or m s−2
Origin
arise from electric charges
Vector forces
both electrical attraction and repulsion are possible (because of positive and negative charges)
Units
F in N, E in N C−1 or V m−1
All gravitational fields
field strength g = mF
i.e. field strength is force per unit mass
All electric fields F field strength E = Q
i.e. field strength is force per unit positive charge
Uniform gravitational fields
parallel gravitational field lines g = constant
Uniform electric fields
parallel electric field lines E = dV = constant
Spherical gravitational fields
radial field lines
force given by Newton’s law:
field strength is therefore:
GMm F = r2
g = GM r2
(Gravitational forces are always attractive, so we show g on a graph against r as negative.)
force and field strength obey an inverse square law with distance
g
r
Spherical electric fields
radial field lines
force given by Coulomb’s law:
field strength is therefore:
Q1Q2 F = 4πε0r2
E = Q 4πε0r2
(A negative charge gives an attractive field, a positive charge gives a repulsive field.)
force and field strength obey an inverse square law with distance
E
positive charge
r
negative charge
Gravitational potential
given by: φ = − GM r
potential obeys an inverse relationship with distance and is zero at infinity
potential is a scalar quantity and is always negative
φ
r
Electric potential
given by: V = Q 4πε0r
potential obeys an inverse relationship with distance and is zero at infinity
potential is a scalar quantity
V
positive charge
r
negative charge
Table 23.1 Gravitational and electric fields compared.
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