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Source of Magnetic Field Ch. 28.

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Source of Magnetic Field Ch. 28

B field of current element (sec. 28.2) Law of Biot and SavartB field of current-carrying wire (sec. 28.3) Force between conductors (sec. 28.4) B field of circular current loop (sec. 28.5) Ampere’s Law (sec. 28.6) Applications of Ampere’s Law (sec. 28.7)

C 2012 J. F. Becker

Learning Goals - we will learn: ch 28

• How to calculate the magnetic field produced by a long straight current- carrying wire, using Law of Biot & Savart. • How to calculate the magnetic field produced by a circular current-carrying loop of wire, using Law of Biot & Savart. • How to use Ampere’s Law to calculate the magnetic field caused by symmetric current distributions.

Magnetic field caused by the current element Idl.

- In figure (b) the current is moving into the screen.

Magnetic field around a long, straight conductor. The field lines are circles, with directions determined by the right-hand rule.

Magnetic field produced by a straight current-carrying wire of length 2a. The direction of B at point P is into the screen.

xo

Law of Biot and SavartdB = mo / 4p (I dL x r) / r3

Use Law of Biot and Savart, the integral is simple!

dB = mo / 4p (I dL x r) / r3

Magnetic field caused by a circular loop of current. The current in the segment dL causes the field dB, which lies in the xy plane.

Magnetic field produced by a straight current-carrying wire of length 2a. The direction of B at point P is into the screen.

xo

Law of Biot and SavartdB = mo / 4p (I dL x r) / r3

Parallel conductors carrying currents in the samedirection attract each other. The force on the upper conductor is exerted by the magnetic field caused by the current in the lower conductor.

Ampere’s Law

Ampere’s Law states that the integral of B around any closed path equals motimes the current, Iencircled, encircled by the closed loop.

Eqn 28.20

We will use this law to obtain some useful results by choosing a simple path along which the magnitude of B is constant, (or independent of dl). That way, after taking the dot product, we can factor out |B|from under the integral sign and the integral will be very easy to do.

See the list of important results in the Summary of Ch. 28 on p. 983

Some (Ampere’s Law) integration paths for the line integral of B in the vicinity of a long straight conductor.

Path in (c) is not useful because it does not encircle the current-carrying conductor.

To find the magnetic field at radius r < R, we apply Ampere’s Law to the circle (path) enclosing the red area. For r > R, the circle (path) encloses the entire conductor.

A section of a long, tightly wound solenoid centered on the x-axis, showing the magnetic field lines in the interior of the solenoid and the current.

COAXIAL CABLEA solid conductor with radius a is insulated from a conducting rod with inner radius b and outer radius c.

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