My lecture slides are posted at ...humanic/p112_lecture11.pdf · 21.7 Magnetic Fields Produced by Currents A solenoid is made up of many current loops which extend a finite distance

My lecture slides are posted at http://www.physics.ohio-state.edu/~humanic/

Information for Physics 112 midterm, Wednesday, May 2 1) Format: 10 multiple choice questions (each worth 5 points) and two show-work problems (each worth 25 points), giving 100 points total. 2) Closed book and closed notes. 3) Can make up your own equation sheet on a single normal sized piece of paper (8.5” x 11"), both sides of sheet -- handwritten -- no worked out problems -- only equations and physical constants allowed -- signed equation sheet must be turned in with the exam 4) Covers the material in Chapters 18, 19, 20 – Electricity only

Chapter 21

Magnetic Forces and Magnetic Fields

21.7 Magnetic Fields Produced by Currents

Right-Hand Rule No. 2. Curl the fingers of the right hand into the shape of a half-circle. Point the thumb in the direction of the conventional current, and the tips of the fingers will point in the direction of the magnetic field.

Currents in wires produce magnetic fields. The long current-carrying vertical wire shown will cause a compass needle to deflect in a circular pattern around the wire in a horizontal plane.


The magnitude of the B-field created from a long, straight wire carrying current I at a distance r from the wire is found experimentally to be,

rI

B o

πµ2

=

AmT104 7 ⋅×= −πµo

permeability of free space Why must the wire be long?

è to avoid fringe field effects.


Example 7 A Current Exerts a Magnetic Force on a Moving Charge The long straight wire carries a current of 3.0 A. A particle has a charge of +6.5x10-6 C and is moving parallel to the wire at a distance of 0.050 m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force on the particle.


θπµ

θ sin2

sin ##$

%&&'

(==

rI

qvqvBF o

rI

B o

πµ2

= Magnetic field at a distance r from the wire with current I

= (6.5 x 10-6)(280) {(4π x 10-7)(3.0)/[2π(0.050)]} sin 90o = 2.2 x 10-8 N From RHR-2 (for B) and RHR-1 (for F), F is radially inward.

Force on a moving charge in a B-field,


Current carrying wires can exert forces on each other.

Calculate the magnitude of the force on Wire 2 due to Wire 1, F21, if the wires carry currents I1 and I2, respectively, and are separated by a distance r. F21 = I2LB21sin θ where B21 = µ0I1/(2πr) is the B-field at 2 from 1 F21 = I2L{µ0I1/(2πr)}sin θ = I1L{µ0I2/(2πr)}sin θ = F12 , the force on 1 by 2 Using RHR-1 and RHR-2 this agrees with Newton’s 3rd law that F12 = - F21

currents in opposite directions currents in same direction


Conceptual Example 9 The Net Force That a Current-Carrying Wire Exerts on a Current Carrying Coil Is the coil attracted to, or repelled by the wire? è answer: attracted to (why?)

× × × × × × ×

× × × ×

B1 (in)


The magnetic field at the center of a loop of wire of radius R with current I is found to be experimentally,

center of circular loop

RI

B o

2µ

=

Find the direction of the B-field at the center by using RHR-2.


Example 10 Finding the Net Magnetic Field A long straight wire carries a current of 8.0 A and a circular loop of wire carries a current of 2.0 A and has a radius of 0.030 m. The wires are adjacent to each other without touching. Find the magnitude and direction of the magnetic field at the center of the loop.


!!"

#$$%

&−=−=RI

rI

RI

rI

B ooo 2121

222 πµµ

πµ

( )( )

T101.1m 030.0

A 0.2m 030.0

A 0.82

AmT104 57

−−

×=##$

%&&'

(−

⋅×=

ππB

B = B1(straight wire) + B2(loop)

Since B1 > B2 , the direction of B is along B1, normal to the current plane.


The field lines around the bar magnet resemble those around the loop. To find the direction of the “phantom North Pole” of a loop, use RHR-2 and the direction of B at the center is also the direction of the “North Pole.”


Loop currents in the same direction, phantom magnets attract.

Loop currents in opposite directions, phantom magnets repel.

è similar behavior as two parallel current-carrying wires.


A solenoid is made up of many current loops which extend a finite distance along the axis of the loops characterized by the number of turns (number of loops) per unit length, n. The B-field in the interior of a long solenoid depends only on n and the current in the loops, I, as

Interior of a long solenoid nIB oµ=

B-field lines similar to those of a bar magnet with N and S poles shown. Use RHR-2

for direction of B inside

(B ~ 0 outside)

21.8 Ampere’s Law

AMPERE’S LAW FOR STATIC MAGNETIC FIELDS For any current geometry that produces a magnetic field that does not change in time, sum up all of the segment lengths Δl multiplied by the B|| è this equals a constant multiplied by the current enclosed by the path. In mathematical notation,

IB oµ=Δ∑ ||

net current passing through surface bounded by path

Note: this is a messy thing to use for anything except in situations where the geometry of the problem has a lot of symmetry, e.g. the long straight wire

21.8 Ampere’s Law Example 11 An Infinitely Long, Straight, Current-Carrying Wire Use Ampere’s law to obtain the magnetic field è lots of symmetry!

IB oµ=Δ∑ ||

( ) IB oµ=Δ∑

IrB oµπ =2

rI

B o

πµ2

= è We get our familiar equation!

Can choose a path where B|| is constant

Since path is a circle of radius r

On RHS, I is the only current enclosed by path

21.9 Magnetic Materials

The intrinsic “spin” and orbital motion of electrons gives rise to the magnetic properties of materials è electron spin and orbits act as tiny current loops.

In ferromagnetic materials groups of 1016 - 1019 neighboring atoms form magnetic domains where the spins of electrons are naturally aligned with each other; magnetic domain sizes are ~ 0.01 - 0.1 mm.

An external magnetic field can induce magnetism in ferromagnetic materials by merging and aligning domains. Depending on the material, the induced magnetism may or may not become permanent. Putting iron in the center of a solenoid can create a strong electromagnet with fields 100x - 1000x the applied fields (also, can turn fields on and off).

21.9 Magnetic Materials

The induced magnetization patterns on the magnetic coating become permanent so the recording can be played back later.

Magnetic tape recording.

Documents

My lecture slides are posted at ...humanic/p112_lecture11.pdf · 21.7 Magnetic Fields Produced by Currents A solenoid is made up of many current loops which extend a finite distance