Direction of Electric Field in a Changing Magnetic Field

In summary, the direction of the electric field at a point to the right of the circular region with a decreasing magnetic field out of the page is towards the bottom of the page. This is determined by Lenz's Law and the right hand rule, and can also be confirmed using the equation ##\nabla\times\vec E = -\frac{\partial}{\partial t}\vec B##.
  • #1
Queequeg
25
0

Homework Statement



In a circular region in the plane of paper, a magnetic field is directed out of the page and decreasing. What is the direction of the electric field at a point to the right of the region?

Homework Equations



Lenz's law

The Attempt at a Solution



Since the magnetic field is decreasing, Lenz's Law states the induced magnetic field will oppose this change, so the induced magnetic field will also point out of the page. So to the right of this region, the right hand rule says that the electric field should point towards the top of the page, but the answer in my key is to the bottom. Am I wrong?
 
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  • #2
The magnetic field is out of the page and decreasing - this would correspond to a south pole facing the page and being drawn away ... so the page should have an induced north pole there, because it wants to pull it back.

Which would put the current circulating anti-clockwise.
Current follows the electric field - so you seem to be right.

You could also work it from ##\nabla\times\vec E = -\frac{\partial}{\partial t}\vec B##
 
  • #3
I agree with posts 1 and 2.
 

Related to Direction of Electric Field in a Changing Magnetic Field

1. What is the direction of an electric field?

The direction of an electric field is the direction that a positive test charge would move if placed in the field. It is represented by arrows pointing away from positive charges and towards negative charges.

2. How is the direction of an electric field determined?

The direction of an electric field is determined by the direction of the force that a positive test charge would experience when placed in the field. The direction of the force is always perpendicular to the electric field lines.

3. Does the direction of an electric field depend on the charge of the particle creating the field?

Yes, the direction of an electric field depends on the charge of the particle creating the field. Positive charges create electric fields that point away from them, while negative charges create electric fields that point towards them.

4. Can the direction of an electric field change?

Yes, the direction of an electric field can change depending on the position and charge of other particles in the vicinity. Electric fields can also be manipulated by external forces, such as magnetic fields.

5. How does the direction of an electric field affect the motion of particles?

The direction of an electric field determines the direction of the force that a charged particle would experience when placed in the field. This force can cause the particle to accelerate or change direction, depending on the initial velocity of the particle and the direction of the field.

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