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Biot-Savart Law

The Biot-Savart Law describes the magnetic field which is generated by an electric current. It related the magnetic field to the magnitude, direction, length and proximity of the electric current present. The law is used in magnetostatic approximation. 

The Biot-Savart law is used for calculating the resultant magnetic field B at position r which is generated by a steady current I. A continual flow of charges is constant in time; the charge neither accumulates nor depletes at any point. The equation is:

B =(u0/4π) ∫C(Idl x r/|r|^3)

Maxwell considered magnetic permeability u to be a measure of the density of the vortex sea. Hence:

  1. Magnetic induction current

B = uH

Was essentially a rotational analogy to the linear electric current relationship

  1. Electric Convection current

J = ρv

Where ρ is electric charge density. B was seen as a kind of magnetic current of vortices aligned in their axial planes, with H being the circumferential velocity of the cortices.

The electric current equation can be viewed as a convective current of electric charge that involved linear motion

The law of Biot and savart

A current flows along a wire that makes a right angle bend, as shown in the figure. If this right angle bend lies at the origin and the wire carrying the incoming current lies on the negative y-axis (and extends to large negative distances), then the part of the wire carrying the outgoing current lies on the positive x axis (and

Physics: Current, Magnetic Field, Vector, and Biot-Savart Law

Magnetic Field from Two Wires Learning Goal: To understand how to use the principle of superposition in conjunction with the Biot-Savart (or Ampere's) law. From the Biot-Savart law, it can be calculated that the magnitude of the magnetic field due to a long straight wire is given by , where ( ) is the permeability constan

Biot Savart Law - Magnetic Field of Circular Loop

A circular loop of radius R is placed in the xy-plane, centered at the origin, as shown. A constant current I flows in the loop. Use the Biot-Savart Law to calculate the H -field along the z-axis. See attached for full problem description.

Permeability of Free Space

State the meaning of permeability, write down the expression for the permeability of free space, and indciate how it was developed from the Biot-Savart Law. Draw the B-H characteristic for: a) a ferromagnetic material b) a non-ferromagnetic material and show how the permeability may be calculated from them.

Ampere's Law: Magnetic field from a wire

Consider a straight section of wire of length L which carries a current I, as shown below. Show that the magnetic field at a point P a distance R from the wire along its perpendicular bisector is B = (muI/2piR) * L/(L^2 + 4R^2)^1/2 ^ : : : : L/2 : I : : :

Magnetic Field due to a Magnetic Dipole

The Earth's magnetic field is essentially that of a magnetic dipole. If the field near the North Pole is about 1.0x10^-4 T, what will be its approximate value 18,000km above the surface at the North Pole?

Magnetic Field - Excel Graph

Consider a flat circular current loop of radius R carrying current I. Chose the X axis to be along the axis of the loop, with the origin at the center of the loop. In MS Excel - Graph the ratio of the magnitude of the the magnetic field at coordinate x to that of the origin, for x = 0 to x=5R.

Biot Savart law

(a) Use the Biot-Savart law for currents to analyze the contributions of segments 1 and 5 to the magnetic field at point P. (b) Compare the contributions of segments 2 and 4 to the magnetic field at point P (both magnitude and direction). (c) The magnetic field at P is a sum of integrals, each one for a single segment of t