Download PHYS219 Fall semester 2014 - Purdue Physics

PHYS219 Fall semester 2014
Lecture 11:
Force on Current-Carrying Wires
Dimitrios Giannios
Purdue University
The Lorentz Force
• The Lorentz Force - the force on a charged particle moving in a
magnetic field
• Coulomb’s Law correctly gives the force between two point charges
when they are at rest.
• When the two charges are in motion, there is an extra force called the
“magnetic force”.
In what follows, we provide a very simple introduction to this magnetic
force.
The magnetic force on a charged particle in a uniform B field
(from systematic experiments)
a) zero
velocity
NO FORCE !
b) velocity
parallel to B
NO FORCE !
c) velocity
perpendicular to B
MAXIMUM FORCE
It’s a cross-wise force!!
Direction of magnetic force on a charged
particle moving in a uniform B field
http://www.conspiracyoflight.com/Lorentz/Lorentzforce.html
The Lorentz Force (1892)
OR
(a)
Focus on the plane
containing v and B
(b)
(c)
(d)
Always chose the smallest angle
between B and v
This implies that a charge q of 1 C
moving with a velocity v of 1 m/s
perpendicular to a magnetic field B of
1 T experiences a force F of 1 N.
What is the magnetic force on the charged
particle?
F
B
v
F
B
v
direction??
for +q charge;
reverse F if q is
negative
Force on a current carrying wire in a B field
1. An electric current is a collection
of moving charges
I= ΔQ/ Δ t
2. From the equation of the force on a
moving charge
F = qvB sinθ
q= Δ Q
v=L/ Δ t
F=(Δ Q)(L/ Δ t)B sinθ
3. The force on a current-carrying wire is
Fon wire =I L B sin θ
4. The direction of the force is given by
the right-hand rule
conventional
current
Example
=1.3 A
L=1.5 m
A 1.5 m long piece of wire is in a
uniform magnetic field of 2 T. If the
wire is carrying a current of
1.3 A, what force will it feel?
=2.0 T
v (or I)
B
F is in -x
direction??
Consequence: MAGNETIC force between
current-carrying wires
X
B
V
Similar Force on wire 2
Parallel currents attract
Wires are electrically
neutral, but still feel
a force!
What is the force between two parallel wires?
(from experiment)
Parallel Currents Attract
Antiparallel Currents Repel
Force on a Current Loop
Equilibrium
Orientation
3
A Home-Made Motor
The general case
line ┴ to plane of loop
Example
line ┴ to plane of loop
A loop of wire with a 15 cm radius is placed in a uniform
magnetic field of 2 T at an angle of 45o. If the wire is carrying a
current of 10 A, what torque will the coil feel?
Lawn mower torques – for comparison?
Craftsman
37436
PRICE:
$430
TORQUE: 7 lb-ft