Answer :
Without the specifics of the potentials in exercises 10.1, 10.3, and 10.4, it's impossible to say which abide by the Coulomb gauge and which abide by the Lorenz gauge. Comparing the potentials with the conditions of each gauge can help determine this. If a potential satisfies the Coulomb condition but not the Lorenz, it's in the Coulomb gauge, and vice versa.
To determine whether a potential is in the Coulomb gauge or the Lorenz gauge, you need to understand each concept.
Coulomb's gauge condition is ∇•A=0, and Lorenz's gauge condition is ∇•A + (1/c²)(∂φ/∂t) = 0 where A is the magnetic vector potential and φ is the electric scalar potential.
It would be necessary to apply these conditions to the potentials given in exercises 10.1, 10.3, and 10.4 respectively.
However, without the specifics of the potentials mentioned in these problems, it's impossible to specifically lay out which ones abide by the Coulomb gauge and which ones abide by the Lorenz gauge.
If a potential satisfies the Coulomb condition but not the Lorenz condition, it is in the Coulomb gauge.
Likewise, if a potential satisfies the Lorenz condition but not the Coulomb condition, it is in the Lorenz gauge.
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