Practice question · Multiple choice
The magnetic field has zero divergence, whereas the static electric field has zero curl. What fundamental mathematical consequence follows for their potentials?
Hints
- What mathematical identity links the curl of a gradient to zero?
- How does the presence or absence of circulation determine whether a scalar potential can be defined?
Show the answer
C. A scalar potential exists for E while B requires a vector potential
Why
Zero divergence prevents B from being a scalar gradient since curl of gradient vanishes, requiring the vector potential B = curl A. Conversely, irrotational E admits a scalar potential. Non-zero curl means circulation does not vanish, precluding conservative scalar descriptions for B.
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