Chapter 29.Magnetic

7/27/2019 Chapter 29.Magnetic

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Chapter 29. Magnetic Field Due to

Currents

29.1. What is Physics?29.2. Calculating the Magnetic Field Due to aCurrent29.3. Force Between Two Parallel Currents29.4. Ampere's Law29.5. Solenoids and Toroids

29.6. A Current-Carrying Coil as a MagneticDipole


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What is Physics?

A moving charged particleproduces a magnetic fieldaround itself


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Magnetic Field Due to a Current

A length vector that haslength dsand whose directionis the direction of the currentin ds.

Thepermeability constant, whose value is defined tobe exactly


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Magnetic Field Due to a Current in a Long Straight

Wire0

2

sin

4

i ds

dB r


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Magnetic field lines produced by a

current in a long straight wire


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Right-hand ruleGrasp the element in yourright hand with yourextended thumb pointing in

the direction of the current.Your fingers will thennaturally curl around in thedirection of the magnetic

field lines due to thatelement.


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Magnetic Field Due to a Current in a

Circular Arc of Wire

2

l l


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A Current-Carrying Coil as a Magnetic Dipole0

2c

iB

R

For a loop , =2, at the center ofthe loop

0

2 2 3/ 2

( )2 ( )

B z

R z

If


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Sample ProblemThe wire in Fig. 29-8acarries a current iand consists ofa circular arc of radius Rand central angle rad, and

two straight sections whose extensions intersect thecenter Cof the arc. What magnetic field does thecurrent produce at C?
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Example Finding the Net Magnetic FieldA long, straight wire carries a current of I1=8.0 A. AsFigure 21.31aillustrates, a circular loop of wire liesimmediately to the right of the straight wire. The loophas a radius of R=0.030 m and carries a current ofI2=2.0 A. Assuming that the thickness of the wires is

negligible, find the magnitude and direction of the netmagnetic field at the center Cof the loop.


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Two Current-Carrying Wires ExertMagnetic Forces on One Another

To find the force on a current-carrying wire due to a

second current-carrying wire, first find the field due tothe second wire at the site of the first wire. Then findthe force on the first wire due to that field.

Parallel currents attract each other, and antiparallelcurrents repel each other.


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Ampere's Law

The loop on the integral sign means that is to be integrated around aclosedloop, called an Amperian loop. The current ienc is the netcurrent encircled by that closed loop.

Curl your right hand around the Amperian loop, with the fingerspointing in the direction of integration. A current through the loop in

the general direction of your outstretched thumb is assigned a plussign, and a current generally in the opposite direction is assigned aminus sign.


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ExampleAn Infinitely Long, Straight,

Current-Carrying WireUse Amperes law to obtain themagnetic field produced by thecurrent in an infinitely long,straight wire.


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Magnetic Field Inside a Long Straight

Wire with uniformly distributed Current


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A LOOP OF Current

For a single loop, the magneticfield at the center is:B=0I/(2R)

For a loop with N turns of wire,


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Comparison a loop wire and a bar magnet loop wire

bar magnet


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Magnetic Field of a Solenoid

For a long ideal solenoid

where nis the number of turns per unit length of the solenoid


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Magnetic Field of a Toroid


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Example

A solenoid is 0.50 m long, has three layers of windingsof 750 turns each, and carries a current of 4.0 A.What is the magnetic field at the center of thesolenoid?


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Example


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Example


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Example


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Example

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Chapter 29.Magnetic