Lecture 27: FRI 20 MAR Magnetic Fields III Physics 2113 Jonathan Dowling “They are not supposed to exist….” Aurora Borealis.

Lecture 27: FRI 20 MARLecture 27: FRI 20 MARMagnetic Fields IIIMagnetic Fields III

Physics 2113

Jonathan Dowling

“They are not supposed to exist….”

Aurora Borealis

Magnetic Force on a Wire.Magnetic Force on a Wire.

L

Magnetic Force on a WireMagnetic Force on a Wire

L

Note: If wire is not straight,compute force on differential elements and integrate:

i

.i

(28-12)

i

28.8.2. A portion of a loop of wire passes between the poles of a magnet as shown. We are viewing the circuit from above. When the switch is closed and a current passes through the circuit, what is the movement, if any, of the wire between the poles of the magnet?

a) The wire moves toward the north pole of the magnet.

b) The wire moves toward the south pole of the magnet.

c) The wire moves upward (toward us).

d) The wire moves downward (away from us into board).

e) The wire doesn’t move.

ExampleExample

By symmetry, F2 will only have a vertical component,

Notice that the force is the same as that for a straight wire of length R,

L LR R

and this would be true nomatter what the shape of the central segment!.

Wire with current i.Magnetic field out of page.What is net force on wire?

i

i

SP28-06

ICPP: Find Direction of B

Example 4: The Rail GunExample 4: The Rail Gun• Conducting projectile of length

2cm, mass 10g carries constant current 100A between two rails.

• Magnetic field B = 100T points outward.

• Assuming the projectile starts from rest at t = 0, what is its speed after a time t = 1s?

• Conducting projectile of length 2cm, mass 10g carries constant current 100A between two rails.

• Magnetic field B = 100T points outward.

• Assuming the projectile starts from rest at t = 0, what is its speed after a time t = 1s?

B I L

• Force on projectile: F= iLB (from F = iL x B)• Acceleration: a = F/m = iLB/m (from F = ma)• v = at = iLBt/m (from v = v0 + at)

= (100A)(0.02m)(100T)(1s)/(0.01kg) = 2000m/s= 4,473mph = MACH 8!

• Force on projectile: F= iLB (from F = iL x B)• Acceleration: a = F/m = iLB/m (from F = ma)• v = at = iLBt/m (from v = v0 + at)

= (100A)(0.02m)(100T)(1s)/(0.01kg) = 2000m/s= 4,473mph = MACH 8!

projectile

rails

Rail guns in the “Eraser” movie"Rail guns are hyper-velocity weapons that shoot aluminum or clay rounds at just below the speed of light. In our film, we've taken existing stealth technology one step further and given them an X-ray scope sighting system," notes director Russell. "These guns represent a whole new technology in weaponry that is still in its infancy, though a large-scale version exists in limited numbers on

battleships and tanks. They have incredible range. They can pierce three-foot thick cement walls and then knock a canary off a tin can with absolute accuracy. In our film, one contractor has finally developed an assault-sized rail gun. We researched this quite a bit, and the technology is really just around the corner, which is one of the exciting parts of the story."

Warner Bros., production notes, 1996.http://movies.warnerbros.com/eraser/cmp/prodnotes.html#tech

Also: INSULTINGLY STUPID MOVIE PHYSICS: http://www.intuitor.com/moviephysics/

Rail guns in Transformers II

Rail guns in Reality!

Electromagnetic Slingshot

These Devices CanLaunch 1000kg ProjectilesAt Mach 100 at a Rate of 1000 Projectiles Per Second.

Using KE = 1/2mv2

This corresponds to an output about 1012 Watts = TeraWatt.

Uses: Put Supplies on Mars 80 days after launch.

Current time to Mars on Ordinary Rocket? 1.5-3 years.

Torque on a Current Loop: Principle behind electric motors.

Net force on current loop = 0

For a coil with N turns,τ = N I A B sinθ, where A is the area of coil

Rectangular coil: A=ab, current = i

But: Net torque is NOT zero!

Magnetic Dipole MomentMagnetic Dipole Moment

N = number of turns in coilA = area of coil.

We just showed: τ = NiABsinθRight hand rule:

curl fingers in direction of current;

thumb points along μDefine: magnetic dipole moment μ

As in the case of electric dipoles, magnetic dipoles tend to align with the magnetic field.

Electric vs. Magnetic DipolesElectric vs. Magnetic Dipoles

-Q

θQE

QE

+Q

p=Qa

Magnetic Dipole MomentMagnetic Dipole Moment

N = number of turns in coilA=area of coil.

We just showed: = NiABsinθRight hand rule:

curl fingers in direction of current;

thumb points along μDefine: magnetic dipole moment μ

As in the case of electric dipoles, magnetic dipoles tend to align with the magnetic field.

τ is biggest when B is at right angles to μ

1 and 3 are “downhill”.2 and 4 are “uphill”.U1 = U4 > U2 = U3

ICPP