Sources of

Magnetic

Field

A CHARGE, A STRAIGHT WIRE, AND A LOOP

Magnetic field of a point charge with constant velocity; Magnetic Field of a Straight Current Carrying Conductor; Magnetic Field of a Circular Current Loop

Magnetic field of a point charge with constant velocity

�⃗�=𝜇04𝜋

|𝑞|𝑣𝑠𝑖𝑛𝜙𝑟 2

𝜇0=4𝜋×10−7𝑇 .

𝑚𝐴

Magnetic Field of a Current Element

𝑑𝐵=𝜇04𝜋

𝐼 𝑑𝑙𝑠𝑖𝑛𝜙𝑟2

Magnetic Field of a Straight

𝐵=𝜇0 𝐼2𝜋𝑟

Current Carrying Conductor

Magnetic Field around the conductor

Magnetic Field of aCircular Current Loop

Magnetic Field on the axis of aCircular Current Loop

𝐵𝑥=𝜇0 𝐼 𝑎

2

2 (𝑥2+𝑎2 )32

Magnetic Field on the axis of aCOIL

𝐵𝑥=𝜇0𝑁𝐼 𝑎

2

2 (𝑥2+𝑎2 )32

of N circular loops

Magnetic Field at the center of aCOIL

𝐵𝑥=𝜇0𝑁𝐼2𝑎

of N circular loops

Magnetic Field of a Straight Current Carrying Conductor

ExampleA long, straight conductor carries a current of 100A. At what distance from the axis of the conductor is the magnetic field caused by the current equal in magnitude to the earth’s magnetic field in Pittsburgh (about 0.5x10-4T)

r= 0.4m

Magnetic Field of a Circular Current Loop

A coil consisting of 100 circular loops with radius 0.60m carries a current of 5.0A.a.) find the magnetic field at a point along the

axis of the coil, 0.80m from the center.b.) along the axis, at what distance from the

center is the field magnitude 1/8 as great as it is at the center?

a) Bx= 1.1x10-4Tb) About 1.34 m or 1.34 radii from the center

Sources

1. Young, Hugh D., and Freedman, Roger A. 2002, Reprinted. University Physics with Modern Physics. 10th ed. Singapore: Pearson Education Asia Pte Ltd. Copyright © 2000 by Addison-Wesley Publishing Longman, Inc.2. Giancoli, Douglas C. 2005, Reprinted. Physics. 5th ed. Singapore: Pearson Education Asia Pte Ltd. Copyright © 1998, 1995, 1991, 1985, 1980 by Prentice-Hall, Inc.3. Hewitt, Paul. 2008. Physical Sciences. 4th ed. New York: McGraw-Hill Companies, Inc.4. Images retrieved at www.physics.sjsu.eduhttp://www.physics.upenn.edu/~mele/archives/webpage151/phys151.s04/phys151/phys151.1/graphics/bfields/currentloop.jpghttp://cdn.phys.org/newman/gfx/news/hires/2013/esaswarminge.jpg