Electric and magnetic fields: help understanding the question

[musicmar]

Homework Statement

An electric field points into the page and occupies a circular region of radius 1.0 m. There are no electric charges in the region, but there is a magnetic field forming closed loops pointing clockwise, as shown. The magnetic-field strength 50 cm from the center of the region is 2.0 uT.
a.)What is the rate of the change of the electric field?
b.) Is the electric field increasing or decreasing?

The Attempt at a Solution

I've attached the diagram. I'm just confused on what the question is asking. What does it mean by "a magnetic field is forming"? A magnetic field does not create/change an electric field unless it itself is changing, but there is no information as to how the magnetic field is changing. Clarification would be appreciated. Thank you.

 

[cepheid]

The Attempt at a Solution

I've attached the diagram. I'm just confused on what the question is asking. What does it mean by "a magnetic field is forming"?

You missed the last two key words. The magnetic field is forming closed loops. It's just describing the shape of the field.

A magnetic field does not create/change an electric field unless it itself is changing, but there is no information as to how the magnetic field is changing. Clarification would be appreciated. Thank you.

It's the other way around in this case. A time-varying electric field generates a magnetic field. That's what's happening here. You can figure out the rate of change of the flux of the electric field through the circular area, since you know the strength of the magnetic field.

 

[musicmar]

But we don't know anything about how it varies with time. I know that's what I'm trying to find. I don't understand how knowing the magnetic field strength at one radius helps.

 

[cepheid]

I think the relevant law that describes the relationship between a time-varying electric field and a magnetic field is Ampere's Law, (specifically the term associated with the "displacement current"). It might help to look there.

 

[musicmar]

Yes, you're right about Ampere's law. I will definitely have to use that equation. But what do I do about the I term. You mentioned "displacement current", but I don't really know what that means.

 

[gneill]

Maxwell to the rescue!

$$\oint \vec{B} \cdot \vec{dl} = \mu_0 \epsilon_0 \frac{d \Phi_E}{dt}$$

 

[cepheid]

As your problem statement says, there are no charges present, and hence there is no actual current (a flow of charges). However, Ampere's law must be extended to include the presence of what is called displacement current, **which is related to the rate of change of the electric field with time.** The full details are here:

http://en.wikipedia.org/wiki/Ampère...law:_the_Maxwell.E2.80.93Amp.C3.A8re_equation

But I assume that, since you're being asked a question like this, your notes or textbook must have something about this, maybe at a simplified level (since the geometry of the problem and the uniformity of the electric field mean that many of these calculus-based equations will simplify drastically).

EDIT: Or somebody could just post the equation for you instead of having you slog through that Wikipedia article section, LOL.