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State Biot-Savart’s law in vector form expressing the magnetic field due to an element dl carrying current 7 at a distance r from the element.

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Biot-Savart's law states that the magnetic field BB at a point due to an infinitesimal current element dldl carrying current II at a distance rr from the element is given by: dB=μ04πI dl×r^r2dB=4πμ0r2Idl×r^ Where: dBdB is the infinitesimal magnetic field vector, μ0μ0...
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Biot-Savart's law states that the magnetic field BB at a point due to an infinitesimal current element dldl carrying current II at a distance rr from the element is given by:

dB=μ04πI dl×r^r2dB=4πμ0r2Idl×r^

Where:

  • dBdB is the infinitesimal magnetic field vector,
  • μ0μ0 is the permeability of free space,
  • II is the current flowing through the element,
  • dldl is the infinitesimal current element vector,
  • r^r^ is the unit vector pointing from the current element to the point where the magnetic field is being calculated,
  • rr is the distance from the current element to the point where the magnetic field is being calculated.

In vector form, Biot-Savart's law can be expressed as:

B=μ04π∫I dl×r^r2B=4πμ0r2Idl×r^

This equation represents the vector sum of the magnetic fields contributed by all infinitesimal current elements along the path of integration.

 
 
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