Concept & Reasoning

Ampère-Maxwell law states ∇×H = J + ∂D/∂t. Taking divergence of both sides gives zero on the left because divergence of a curl is always zero. On the right, ∇·J + ∂(∇·D)/∂t = 0. Gauss' law gives ∇·D = ρv. Substituting produces ∇·J + ∂ρv/∂t = 0, the differential continuity equation expressing conservation of charge. Thus the two field laws used are Ampère-Maxwell and Gauss.

How to Solve It in the Exam

Continuity equation = divergence of Ampère-Maxwell + Gauss law.

Important Exam Point

Remember the vector identity ∇·(∇×H)=0.

Quick Trick

Continuity equation = divergence of Ampère-Maxwell + Gauss law.

Common Mistake

Ohm's law is not required to derive charge continuity.

Concept & Reasoning

Ampère-Maxwell law states ∇×H = J + ∂D/∂t. Taking divergence of both sides gives zero on the left because divergence of a curl is always zero. On the right, ∇·J + ∂(∇·D)/∂t = 0. Gauss' law gives ∇·D = ρv. Substituting produces ∇·J + ∂ρv/∂t = 0, the differential continuity equation expressing conservation of charge. Thus the two field laws used are Ampère-Maxwell and Gauss.

How to Solve It in the Exam

Continuity equation = divergence of Ampère-Maxwell + Gauss law.

Important Exam Point

Remember the vector identity ∇·(∇×H)=0.

Quick Trick

Continuity equation = divergence of Ampère-Maxwell + Gauss law.

Common Mistake

Ohm's law is not required to derive charge continuity.

Concept & Reasoning

Ampère-Maxwell law states ∇×H = J + ∂D/∂t. Taking divergence of both sides gives zero on the left because divergence of a curl is always zero. On the right, ∇·J + ∂(∇·D)/∂t = 0. Gauss' law gives ∇·D = ρv. Substituting produces ∇·J + ∂ρv/∂t = 0, the differential continuity equation expressing conservation of charge. Thus the two field laws used are Ampère-Maxwell and Gauss.

How to Solve It in the Exam

Continuity equation = divergence of Ampère-Maxwell + Gauss law.

Important Exam Point

Remember the vector identity ∇·(∇×H)=0.

Quick Trick

Continuity equation = divergence of Ampère-Maxwell + Gauss law.

Common Mistake

Ohm's law is not required to derive charge continuity.