Ampere's law vs. Biot-Savart law

In summary, Ampere's law is a special case of Biot-Savart law and is only applicable in very specific situations, such as straight wires. Biot-Savart law, on the other hand, is more fundamental and can be applied to a wider range of scenarios, including sheets of current and solenoids. However, Ampere's law is often used due to its simplicity and symmetry in certain problems. In addition, there may be errors in calculations when using Ampere's law, such as the presence of pi in the answer.
  • #1
kasse
384
1
What's the difference? Is Ampere's law a special case (when the conductor carrying the current is a straight wire?)
 
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  • #2
Biot-Savart law is the more important and fundamental one. Ampere's law can be derived from it but can only be used in some very specific situations, but not only in straight wire cases. It can be applied to sheets of current, solenoids, etc.
 
  • #3
Mephisto said:
Biot-Savart law is the more important and fundamental one. Ampere's law can be derived from it but can only be used in some very specific situations, but not only in straight wire cases. It can be applied to sheets of current, solenoids, etc.

OK, thanks. Btw, isn't the last calculation wrong here: http://planetphysics.org/encyclopedia/QuarterLoopExampleOfBiotSavartLaw.html

There should be no "pi" in the answer if I'm right.
 
  • #4
Ampere's law is usually only applied to problems that have certain symmetry.

For example, a straight wire is symmetric about it's center axis, a sheet is symmetric, a solenoid is symmetric, etc...

Some arbitrary wire is not symmetric however and Ampere's law can generally not be used there.

Also if you only have a short solenoid or wire for example (a short length in relation to it's radius) then Ampere's law does not give a very accurate answer either, because it ignores the fact that the magnetic field lines curve away from the wire at the ends; it assumes the magnetic field is nearly constant.About the link, if the calculation up until the integral is correct then yes, the pi should cancel indeed. I haven't checked what they did before that though, but I think it's correct (so the pi is wrong).
 

1. What is the difference between Ampere's law and Biot-Savart law?

Ampere's law is a mathematical equation that relates the magnetic field around a closed loop to the electric current passing through the loop. Biot-Savart law also relates the magnetic field to the current, but it is used for calculating the magnetic field at a specific point in space.

2. When should I use Ampere's law and when should I use Biot-Savart law?

Ampere's law is typically used in situations where the current is constant and the magnetic field is symmetric, such as in a long straight wire or a circular loop. Biot-Savart law is used when the current and magnetic field are not symmetric, such as in a current-carrying wire with bends or in a solenoid.

3. Which law is more accurate, Ampere's law or Biot-Savart law?

Both laws are equally accurate and are derived from Maxwell's equations. However, Biot-Savart law can be more complicated to use in certain situations, so Ampere's law is often preferred for simplicity.

4. Can Ampere's law and Biot-Savart law be used for both steady currents and changing currents?

Both laws can be used for steady currents, but only Ampere's law can be used for changing currents. Biot-Savart law requires the current to be constant in order to accurately calculate the magnetic field.

5. Are Ampere's law and Biot-Savart law the only ways to calculate magnetic fields?

No, there are other mathematical equations and methods for calculating magnetic fields, such as the magnetic scalar potential and the magnetic vector potential. However, Ampere's law and Biot-Savart law are two of the most commonly used methods in basic electromagnetic theory.

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