1 / 15

# Sources of Magnetic Fields - PowerPoint PPT Presentation

Sources of Magnetic Fields. Besides magnetic poles, electric currents create magnetic fields. There are two ways of calculating B produced by currents: Biot-Savart Law : Field of a “current element” (analogous to a point charge in electrostatics).

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Sources of Magnetic Fields' - querida-carvalho

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Besides magnetic poles, electric currents create magnetic fields.

• There are two ways of calculating B produced by currents:

• Biot-Savart Law: Field of a “current element”

• (analogous to a point charge in electrostatics).

• Ampère’s Law: An integral theorem similar to

• Gauss’s law.

r

dB

r

θ

I

I

ds

(“permeability of vacuum”)

We getthe total B by integrating ds along the wire:

When is dB=0 ?

How does dB vary with r ?

What is the direction of B at points a and b ?

a

Current I in a straight wire

b

Find B at a distance R from a long straight wire

y

dB

r

f

R

θ

I

x

dx

(note sin θ = R/r = cos f)

Result: the magnitude of the field produced at a distance R from a long straight wire is:

The field lines form circles around the wire. Note the right-hand rule.

I

I

P

a

I

What is the field at point P?

• m0I/(4pa)

• m0I/(2pa)

• m0I/(pa)

• zero

• none of the above

• Circular loop in y-z plane. Find B.

• at the origin

• at point (x, 0, 0)

y

I

R

x

(x, 0, 0)

z

y

At the Origin:

dS

R

r

z

dB

I

Pick a short segment ds where the wire crosses the y – axis:

I ds

dB

θ

r

R

θ

x

θ

r’

θ

dB’

x

I ds’

I

B

B

N

S

current loop

bar magnet

I

I

θo

R2

R1

O

• Find the magnetic field at point O due to the current in the circuit. (Use the Biot-Savart Law on each segment)

• b) Evaluate the expression for:

• I = 20A, R1 = 10cm, R2 = 30cm, θo=120º