# Problem: The magnetic field inside a solenoid can be found exactly using Ampère's law only if the solenoid is infinitely long. Otherwise, the Biot-Savart law must be used to find an exact answer. In practice, the field can be determined with very little error by using Ampère's law, as long as certain conditions hold that make the field similar to that in an infinitely long solenoid.Which of the following conditions must hold to allow you to use Ampère's law to find a good approximation?Consider only locations where the distance from the ends is many times D.Consider any location inside the solenoid, as long as L is much larger than D for the solenoid.Consider only locations along the axis of the solenoid.HintsThe magnetic field inside a solenoid can be found exactly using Ampère's law only if the solenoid is infinitely long. Otherwise, the Biot-Savart law must be used to find an exact answer. In practice, the field can be determined with very little error by using Ampère's law, as long as certain conditions hold that make the field similar to that in an infinitely long solenoid.Which of the following conditions must hold to allow you to use Ampère's law to find a good approximation?Consider only locations where the distance from the ends is many times .Consider any location inside the solenoid, as long as  is much larger than  for the solenoid.Consider only locations along the axis of the solenoid.a onlyb onlyc onlya and ba and cb and c

###### FREE Expert Solution

Ampere's law:

$\overline{){\mathbf{\oint }}{\mathbf{B}}{\mathbf{·}}{\mathbf{d}}{\mathbf{s}}{\mathbf{=}}{{\mathbf{\mu }}}_{{\mathbf{0}}}{{\mathbf{I}}}_{\mathbf{e}\mathbf{n}\mathbf{c}\mathbf{l}\mathbf{o}\mathbf{s}\mathbf{e}\mathbf{d}}}$

The Ampere's path must pass through r and have symmetry.

Ampere's law only holds for an infinitely long solenoid.

This implies that this is possible only for cases where the distance from the ends is many times D.

This condition makes the field to be uniform at every point of the solenoid.

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###### Problem Details

The magnetic field inside a solenoid can be found exactly using Ampère's law only if the solenoid is infinitely long. Otherwise, the Biot-Savart law must be used to find an exact answer. In practice, the field can be determined with very little error by using Ampère's law, as long as certain conditions hold that make the field similar to that in an infinitely long solenoid.

Which of the following conditions must hold to allow you to use Ampère's law to find a good approximation?

Consider only locations where the distance from the ends is many times D.

Consider any location inside the solenoid, as long as L is much larger than D for the solenoid.

Consider only locations along the axis of the solenoid.

Hints

The magnetic field inside a solenoid can be found exactly using Ampère's law only if the solenoid is infinitely long. Otherwise, the Biot-Savart law must be used to find an exact answer. In practice, the field can be determined with very little error by using Ampère's law, as long as certain conditions hold that make the field similar to that in an infinitely long solenoid.

Which of the following conditions must hold to allow you to use Ampère's law to find a good approximation?

Consider only locations where the distance from the ends is many times .

Consider any location inside the solenoid, as long as  is much larger than  for the solenoid.

Consider only locations along the axis of the solenoid.

 a only b only c only a and b a and c b and c

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Ampere's Law concept. If you need more Ampere's Law practice, you can also practice Ampere's Law practice problems.

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Based on our data, we think this problem is relevant for Professor Pickett's class at Abilene Christian University.