1. Force on Current-Carrying Wires
PHYS219 Fall semester 2014
Lecture 11:
Force on Current-Carrying Wires
Dimitrios Giannios
Purdue University

2. 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.

3. (from systematic experiments)
The magnetic force on a charged particle in a uniform B field
(from systematic experiments)
b) velocity parallel to B
c) velocity perpendicular to B
a) zero velocity
MAXIMUM FORCE
NO FORCE !
NO FORCE !
It’s a cross-wise force!!

4. Direction of magnetic force on a charged particle moving in a uniform B field

5. Always chose the smallest angle between B and v
The Lorentz Force (1892) OR
(c)
(b)
(d)
(a)
Always chose the smallest angle between B and v
Focus on the plane containing v and B
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.

6. for +q charge; reverse F if q is negative
What is the magnetic force on the charged particle? F B v B F v
for +q charge; reverse F if q is negative
direction??

7. Force on a current carrying wire in a B field
conventional current
1. An electric current is a collection of moving charges
I= ΔQ/ Δ t
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
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

8. Example
L=1.5 m
=1.3 A
=2.0 T
F is in -x
v (or I) B
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?
direction??

9. Wires are electrically neutral, but still feel a force!
Consequence: MAGNETIC force between current-carrying wires X B V
Similar Force on wire 2
Wires are electrically neutral, but still feel a force!
Parallel currents attract

10. Parallel Currents Attract Antiparallel Currents Repel
What is the force between two parallel wires?
(from experiment)
Parallel Currents Attract Antiparallel Currents Repel

11. Force on a Current Loop
Equilibrium Orientation 3

12. A Home-Made Motor

13. The general case
line ┴ to plane of loop

14. 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?

15. Lawn mower torques – for comparison?
Craftsman PRICE: $430
TORQUE: 7 lb-ft