# Electric field from current without Maxwell's law of induction

A long, straight wire carries a current that decreases linearly with time. What is the direction of the induced electric field outside the wire?

I would interpret this as follows: a current induces a magnetic field. Since the current is changing, the magnetic field is changing, which induces a changing electric field by Maxwell's law of induction.

However, this question was not posed in a context where one would be assumed to know Maxwell's law of induction (a high school science contest, and the law is only covered in the most advanced high school physics courses), which makes me wonder whether this is poorly phrased and simply referring to the electric field set up by the charges in the wire.

I'd greatly appreciate help.

• I wouldn't be surprised if it were indeed referring to the Maxwell-Faraday law. After all, it's a contest, so it's supposed to be for people who know more than the usual curriculum, no? – Brian Bi Feb 25 '14 at 2:30

## 2 Answers

A long straight wire is also an inductor, with the direction of the magnetic field outside of the wire circulating in a direction determined by the right hand rule.

Such a wire doesn't have very much inductance (like a solenoid for instance), so it is not unreasonable to expect that the current through it could be decreased linearly.

When the current passes zero, the magnetic field surrounding the wire collapses, and due to Lenz's law, will induce an electric field in the wire in the direction opposite that of the original current flow (the answer).

In solenoids that are part of an LRC circuit, it is not unusual for this arrangement to produce "ringing", which is a continuation of this process in which there can be several cycles of damped alternating current produced, magnetic field generation and collapse.

I think that the Le Chatelier's principle is enough... The induced electrical field tends to reduce the causes that created it. In this case, effects are the decrease of current, so the induced electrical field tends to increase the current. I don't think there is a difference between inside and outside the wire (inductor effect) (the word outside is maybe specified because the linear slope is assumed).