Mar 7, 2012

Sources of magnetic field

Magnetic field of a moving charge

✤ A charge at rest is surrounded by an electric field.

✤ A charge in motion is surrounded by both an electric field and a magnetic field.

✤ The magnetic field lines circulate around the velocity vector.

Valid for v<<c

Biot-Savart law

✤ In a length dl of a circuit bearing current I, total charge dq moves with average speed v with dq v = I dl.

✤ The magnetic field is the superposition of the fields of the moving charges as expressed by the Bio-Savart Law.

The magnetic field around a current carrying wire

✤ Current comes out of the page

Pick form of currenthttp://www.falstad.com/vector3dm/

Magnetic field of a wire segment

✤ The magnetic field of the current in a straight segment may be found by integration.

✤ The integration may be done in cartesian coordinates or, through a change of variables, in terms of the angle shown.

Magnetic field of a straight wire✤ The field of an infinitely log

wire follows from that for a segment.

✤ The magnetic field of an infinitely long straight current bearing wire is the same everywhere along its length.

✤ It circulates in the azimuthal direction and is proportional to the inverse of the distance r from the wire in cylindrical coordinates.

Magnetic force between parallel conductors

✤ Given the magnetic field due to one circuit (derived using the Biot-Savart Law), we can find the force and torque on another circuit.

✤ For example, for two parallel wires, the force per unit length on current I1 in a field B2 due to a current I2 is

✤ dF1,2/dl = I1B2 ~I1I2.

Magnetic field of a loop

✤ Consider the magnetic field on the axis of a circular current loop.

✤ By symmetry, on the axis, only the axial component is non-vanishing.

✤ Each equal length element of the loop gives the same axial field contribution.

Field of loops

✤ The full field of a current loop may be calculated.

✤ Notice how it resembles that of a magnetized piece of steel.

✤ The field of a helical coil is approximately that of a stack of current loops.

Magnetic flux

✤ We define the flux of magnetic field through a surface element dA as B.dA in a way similar to the flux of electric field.

✤ Magnetic field lines always circulate. There are no magnetic charges from which field lines emerge or disappear. The magnetic analog of Gauss’s Law for electric fields states that the total magnetic flux exiting any closed surface vanishes.