# Spatial dependence of induced Electric field

• shahbaznihal

#### shahbaznihal

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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shahbaznihal said:
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?
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##

Thanks a bunch!

## 1. What is spatial dependence of induced electric field?

The spatial dependence of induced electric field refers to how the strength and direction of an electric field varies across space due to the presence of a changing magnetic field. This phenomenon is described by Faraday's law of induction, which states that a changing magnetic field induces an electric field in the surrounding space.

## 2. How is the spatial dependence of induced electric field measured?

The spatial dependence of induced electric field can be measured using instruments such as voltmeters or oscilloscopes. These devices can detect the presence and strength of an electric field at different points in space.

## 3. What factors affect the spatial dependence of induced electric field?

The spatial dependence of induced electric field is affected by several factors, including the strength and direction of the changing magnetic field, the distance from the source of the magnetic field, and the electrical conductivity of the surrounding materials.

## 4. What are some real-world applications of the spatial dependence of induced electric field?

The spatial dependence of induced electric field has many practical applications, such as in generators and transformers, where it is used to convert mechanical energy into electrical energy. It is also used in medical devices, such as MRI machines, and in wireless charging technology.

## 5. How can the spatial dependence of induced electric field be controlled or manipulated?

The spatial dependence of induced electric field can be controlled or manipulated through the use of materials with different electrical properties, such as conductors and insulators. Additionally, by altering the strength and direction of the changing magnetic field, the induced electric field can be controlled and directed to specific locations.