Goal: To understand Electromagnetic fields

1
Goal To understand Electro-magnetic fields

• Objectives
• Electro-Magnetic Fields
• Magnetic Force on a wire
• Magnetic Field for a straight wire
• Magnetic Field from a coiled wire
• Solenoids
• How to create your own magnet!

2
Electro-Magnetic Fields

• Magnetic Fields tend to occur in the presence of
  electric fields when there are moving charges.
• In fact Magnetic Fields are created to offset the
  electric field and the moving charges!
• Conversely a magnetic field can induce an
  electric current but that is tomarrow.

3
EM Force

• Fe q E
• Fb q V X B
• So F q E qV X B
• To cancel this out V has to be in the direction
  (or opposite to) the electric field.
• So, for F to be 0 then you need v E/B

4
Magnetic Force on a wire

• If a wire is in a magnetic field then there will
  be a force exerted on it!
• F q VXB
• But, I q / t
• So, qV q L / t I L
• So, F I L X B

5
Direction of the force

• But what about the direction the force?
• The current is moving up or down the wire.
• For a wire, the magnetic field circles the wire
  in a direction counter clockwise to the direction
  of the current.
• One way to remember this is to use you hand and
  your thumb is the current.
• The field is your closed hand (give the magnetic
  field a thumbs up!)
• The force is in the direction of LXB
• So, it will always be towards or away from the
  wire.

6
Magnetic Fields from a wire

• A wire with charge will create a magnetic field!
• As you get further from the wire this field will
  do down.
• However, the amount of the wire that affects you
  increases a little (so you get over distance
  instead of distance squared).
• B µ0 I / (2p r)
• Where µ0 4 p 10-7 Tm/A (permeability of free
  space)

7
2 Wire example

• Suppose we have 2 parallel wires leading in the
  x direction.
• The current through both wires is 3 A.
• They are separated by a distance of 0.1 m.
• What is the magnitude and direction of the
  magnetic field exerted on the top wire by the
  bottom wire?

8
2 Wire example

• Suppose we have 2 parallel wires leading in the
  x direction.
• The current through both wires is 3 A.
• They are separated by a distance of 0.1 m.
• What is the magnitude and direction of the
  magnetic field exerted on the top wire by the
  bottom wire?
• B µ0 I / (2p r)
• B 4 p 10-7 Tm/A 3A / (2p 0.1m)
• B 6 10-6 T and from right hand rule in the z
  direction

9
2 Wire example - force

• Suppose we have 2 parallel wires leading in the
  x direction.
• The current through both wires is 3 A.
• They are separated by a distance of 0.1 m.
• B 6 10-6 T and from right hand rule in the z
  direction
• What is the magnitude and direction of the
  magnetic force exerted on the top wire by the
  bottom wire for a 1m segment of the wire?
• Note in HW they will so F/L for this and give
  you some value in N/m for F/L.

10
2 Wire example - force

• Suppose we have 2 parallel wires leading in the
  x direction.
• The current through both wires is 3 A.
• They are separated by a distance of 0.1 m.
• B 6 10-6 T and from right hand rule in the z
  direction
• What is the magnitude and direction of the
  magnetic force exerted on the top wire by the
  bottom wire for a 1m segment of the wire?
• F I LXB 3A 1m 6 10-6 T 1.8 10-5 N
• Direction? Well L is in the X direction and B
  is in the Z direction.
• Right hand rule
• F is in the y direction (down)

11
Magnetic field from a circular current loop

• This one is the opposite of the straight wire in
  terms of finding direction.
• The loop makes a plane.
• The magnetic field will be perpendicular to that
  plane.
• Use your right hand.
• Your curled fingers are the current.
• Note it is counterclockwise.
• Your thumb in this case is the magnetic field.

12
Magnetic field equation

• Lets suppose you have N loops (N can equal 1).
• Inside the loop
• B µ0 N I / (2 r)
• And here r is the radius of the loop not the
  distance from the loop.

13
Solenoids

• You can add a lot of loops over some extended
  length and get a solenoid.
• MRI machines are solenoids.
• Inside the solenoid B µ0 N I / (L)
• L here is the length of the solenoid.
• Notice that it does not depend on the radius of
  the solenoid.
• Also, N/L n (n is often quoted in the
  homework).

14
Build a Magnet!

• Tired of loosing those screws?
• Magnetize your screwdriver!
• But how?
• Well, just wrap a wire around the screwdriver,
  then connect both ends of the wire to a power
  supply (such as a battery, but not too powerful
  or you might hurt yourself).
• Leave it on for some time, few minutes, and when
  you turn it off you will have yourself a
  magnetized screwdriver!
• No more dropping screws into your computers
  power supply

15
Conclusion

• We have learned how to find electromagnetic
  forces.
• We have examined the magnetic fields from
  straight and looped wires as well as solenoids.
• We learned how to use the Right Hand Rule to find
  the direction the current and magnetic fields for
  wires.
• We have seen how to find the force exerted on
  wires.
• We have discovered how to build our own magnets!