Goal: To understand Electro- magnetic fields Objectives: 1)Learn what Electro-Magnetic Fields are 2)Learn how to calculate the Magnetic Force on a wire 3)Learn to find the Magnetic Field for a straight wire 4)Learn to calculate the Magnetic Field from a coiled wire 5)To learn about Solenoids 6)Learn how to create your own magnet!

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 tomorrow.

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

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.

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 = μ 0 I / (2π r) Where μ 0 = 4 π * Tm/A (permeability of free space)

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?

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 = μ 0 I / (2π r) B = 4 π * Tm/A * 3A / (2π 0.1m) B = 6 * T and from right hand rule in the +z direction

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 * 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.

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 * 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 * T = 1.8 * 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)

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.

Magnetic field equation Lets suppose you have N loops (N can equal 1). Inside the loop: B = μ 0 N I / (2 r) And here r is the radius of the loop not the distance from the loop.

Solenoids You can add a lot of loops over some extended length and get a solenoid. MRI machines are solenoids. Inside the solenoid B = μ 0 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).

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 computer’s power supply…

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!