Why is Biot-Savart Law Zero for Cylinderical Uniform Current Density?

In summary, the Biot-Savart Law, which describes the magnetic field produced by a current-carrying wire, becomes zero for a cylindrical uniform current density due to symmetry. This refers to a situation where the current is flowing uniformly through a cylindrical wire. It is always zero in this case, making it unusable for calculating the magnetic field. Understanding this concept is important in explaining the behavior of magnetic fields and emphasizing the role of symmetry in applying the Biot-Savart Law.
  • #1
hokhani
504
8
if you want to calculate the magnetic field of a cylinderical uniform current density
by Biot-savart law,
it will be zero, but by Ampere law it is not zero?
why?
please guide me
 
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  • #2
hokhani said:
if you want to calculate the magnetic field of a cylinderical uniform current density
by Biot-savart law,
it will be zero,
Why do you say that?
 
  • #3
oh sorry
I made a mistake
 

FAQ: Why is Biot-Savart Law Zero for Cylinderical Uniform Current Density?

Why is the Biot-Savart Law zero for a cylindrical uniform current density?

The Biot-Savart Law is a fundamental principle in electromagnetism that describes the magnetic field produced by a current-carrying wire. However, in the case of a cylindrical uniform current density, the Biot-Savart Law becomes zero because the magnetic field produced by each infinitesimal element of the wire cancels out due to symmetry.

What is a cylindrical uniform current density?

A cylindrical uniform current density refers to a situation where the current is flowing uniformly through a cylindrical wire. This means that the current has the same magnitude and direction at every point along the wire.

Is the Biot-Savart Law always zero for a cylindrical uniform current density?

Yes, the Biot-Savart Law is always zero for a cylindrical uniform current density. This is because the magnetic field produced by each infinitesimal element of the wire always cancels out due to the symmetry of the current distribution.

Can the Biot-Savart Law be used to calculate the magnetic field for a cylindrical uniform current density?

No, the Biot-Savart Law cannot be used to calculate the magnetic field for a cylindrical uniform current density because it becomes zero in this case. Instead, other methods such as Ampere's Law or the magnetic field due to a solenoid formula can be used to calculate the magnetic field in this scenario.

Why is it important to understand why the Biot-Savart Law is zero for a cylindrical uniform current density?

Understanding why the Biot-Savart Law is zero for a cylindrical uniform current density is important because it helps to explain the behavior of magnetic fields in this specific situation. It also highlights the importance of considering symmetry when applying the Biot-Savart Law to calculate magnetic fields.

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