1. Magnetic Fields and Forces
Chapter 20
Magnetic Fields and Forces

2. Review Magnetic fields Are due to moving charges
Right-hand rule 1
Act similar to electric fields with important differences
Field lines make loops from north to south poles
No magnetic mono-poles
Force is perpendicular to direction of field
Exert a force on moving charges
Right-hand rule 2

3. Right-Hand Rule
Right-hand Rule 1 gives direction of Magnetic Field due to current
Right-hand Rule 2 gives direction of Force on a moving positive charge
Section 20.1

4. Right-hand Rule 1
What is the direction of the magnetic field in regions 1, 2 and 3?
B1 and B3 are non-zero
They would be zero if these were two sheets of current 1 I 2 I 3

5. Right-hand Rule 1

6. Right-hand Rule 2
What is the direction of the force on a charge moving perpendicular to an external magnetic field?
What is the radius of the circle formed by the charge’s trajectory?
Section 20.3

7. Mass Spectrometer
Uses magnetic forces to separate particles by mass and charge
Ions with different masses will travel in arcs with different radii
Used to find the composition of a material
Calculate charge to mass ratio
Section 20.6

8. Example: Bubble Chamber
Used in particle physics to investigate decay products
What is the sign of the charge?
What is the relative mass?

9. Hall Effect
(+) charge moving to the right and (-) charge moving to the left produce the same current direction
The Hall Effect can distinguish between the two options
Section 20.6

10. Hall Effect, cont.
For a current carrying wire in a perpendicular magnetic field, net charge will accumulate on the top and bottom of the wire
Measuring the potential difference between top and bottom will indicate the sign of the charge carriers
Section 20.6

11. Example: Hall Effect I V d
What is the magnitude and direction of the magnetic field?
ncopper = 8.47 x 1028 m-3
Side View I V
Front View d

12. Magnetic Force on a Current
An electric current is a collection of moving charges
Obeys magnetic force law
From the equation of the force on a moving charge, the force on a current-carrying wire is
The direction of the force is given by the right-hand rule 2
Section 20.4

13. Ampère’s Law
Ampère’s Law can be used to calculate the magnetic field when there is symmetry
Similar to Gauss’ Law for electric fields
Relates the magnetic field along a path to the electric current enclosed by the path
Section 20.7

14. Ampère’s Law, cont.
The magnetic field along a closed path is related to the current enclosed by that path
μo is the permeability of free space
μo = 4 π x T . m / A
If B varies in magnitude or direction along the path, Ampère’s Law is not useful
Section 20.7

15. Magnetic Field of a Long Straight Wire
Ampère’s Law can be used to find the magnetic field near a long, straight wire
Choose a circular, closed path
B|| is the same all along the path
If the circular path has a radius r, then the total path length is 2 π r
Applying Ampère’s Law gives
Section 20.7

16. Example: Two Parallel Wires
What is the force on wire 1 due to wire 2?
Is the force attractive or repulsive?
(Demonstration) I 1 L r 2 I

17. Field from a Current Loop
It is not possible to find a simple path along which the magnetic field is constant
Ampère’s Law cannot be easily applied
From other techniques,
Section 20.7

18. Field Inside a Solenoid
By stacking many loops close together, the field along the axis is much larger than for a single loop
A helical winding of wire is called a solenoid
More practical than stacking single loops
For a long solenoid, there is practically no field outside
Section 20.7

19. Example: Long Solenoid
What is the magnetic field, B, inside a “long” solenoid?

20. Torque on a Current Loop
A magnetic field can produce a torque on a current loop
Assume a square loop with sides of length L carrying a current I in a constant magnetic field
The directions of the forces can be found from right-hand rule 2
Section 20.5

21. Torque, cont.
On two sides, the current is parallel or antiparallel to the field, so the force is zero on those sides
The forces on sides 1 and 3 are in opposite directions and produce a torque on the loop
When the angle between the loop and the field is θ, the torque is
τ = I L2 B sin θ
For different shapes, this becomes
τ = I A B sin θ
Section 20.5

22. Magnetic Moment, μ τ = μ B sin θ
For a current loop, the magnetic moment, μ, is I A
The direction of the magnetic moment is either along the axis of the bar magnet or perpendicular to the current loop
The strength of the torque depends on the magnitude of the magnetic moment
τ = μ B sin θ
Section 20.5

23. Electric Motor A magnetic field can produce a torque on a current loop
If the loop is attached to a rotating shaft, an electric motor is formed
In a practical motor, a solenoid is used instead of a single loop
Additional set-up is needed to keep the shaft rotating
Section 20.10

24. Electric Generator Electric generators are closely related to motors
A generator produces an electric current by rotating a coil between the poles of the magnet
A motor in reverse
Section 20.10