# Spatial dependence of induced Electric field

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## Main Question or Discussion Point

The Faraday's law and Lenz's law together give you, $$\xi = -\frac{\partial\phi_B}{\phi t}$$ or put another way,$$\vec{\nabla} \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$$. My question, I am just asking to make sure, the spatial dependence of $\vec \nabla \times \vec E$ will be the same as the spatial dependence of $\vec B$. So for example, if in a problem, the spatial extent of the magnetic field is restricted to a certain area then it is correct to assume that the closed lines of induced electric field will also be limited (circling the same) to the spatial extent of the magnetic field. Correct?

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No. In such a case $\nabla \times E$ will be spatially limited, but not necessarily E. The spatial extent of E is not the same as the spatial extent of $\nabla \times E$