# Magnetic Field Outside Infinite Solenoid

## Homework Statement

See figure attached.

The author claims the field outside this infinitely long solenoid with N' turns and a current i(t) flowing through it is 0, but he doesn't explain why.

Why is it 0? Is there an intuitive reasoning behind it?

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## The Attempt at a Solution

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#### Attachments

• EX4.13.JPG
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It's NOT zero.

[PLAIN]http://img266.imageshack.us/img266/3547/solenoidlarge.jpg [Broken]

Because there is a magnetic field outside of a solenoid, a solenoid made from a solenoid actually has a magnetic field!

For all practical purposes for a linear solenoid, this is a very good approximation:

[PLAIN]http://img215.imageshack.us/img215/4861/solenoid.jpg [Broken]

Infinite solenoids have no ends, so the circular loops you see coming out of the ends of the solenoid aren't there in the simplification.

The intuitive reasoning behind this is that when you deform the pseudo-ellipse shaped loop of the exterior solenoid field, a single loop will approach hemispheres. Not only will the arc of the hemisphere be infinitely far away from any point in along the solenoid, since the solenoid is infinitely long, there will never be lines emerging from the ends of the solenoid.

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