Goal: To understand Electro-magnetic fields

Objectives:1) To learn about Magnetic Fields

2) To be able to calculate the magnitude of Magnetic Forces

3) To know how to use the Right Hand Rule to get the direction of the magnetic force

4) To understand Motions of particles in a Magnetic field

5) To learn about Cyclotrons

Magnetic Fields

• Just like with electric fields and gravitational fields, magnetic fields are an indicator of the magnetic topography of the region.

• One example to illustrate this is the magnetic dipole or bar magnet.

Bar magnets

• All have 2 ends, North and South

• This is like + and – for charges.

• This creates a field where charges for from the north pole to the south pole just like they went from + charge (high potential) to – (low potential)

Magnetic Field Lines

• Much like we had electric field lines we have magnetic field lines.

• These are the lines which charges would follow (sort of).

• These are the lines that charges or magnetic materials would follow

Earth’s magnetic field (NASA)

Magnetic Force

• The magnetic force is very complicated.• With electric fields the force is towards

charges usually.• However, with magnetic forces, the force

is PERPENDICULAR to the magnetic field.

• But before we examine that lets look at the equation…

Magnetic Force Equation

• F = q V X B

• But V X B isn’t normal multiplication because V and B are vectors.

• Turns out if V and B are in the same direction (the angle between them is 0), then V X B are 0.

• Conversely if the angle is 90 degrees then you just multiply as normal.

• So, F = qvBsin(θ) where θ is the angle between the vectors v and B.

Okay first an example for the MAGNITUDE of the force

• For most of what we will do velocity and B will be perpendicular.

• Lets assume that to be true here.

• If the charge is 4C, the velocity is 200 m/s, and B is 0.1 Tessla (T) then what is the magnitude of the force?

Okay first an example for the MAGNITUDE of the force

• For most of what we will do velocity and B will be perpendicular.

• Lets assume that to be true here.

• If the charge is 4C, the velocity is 200 m/s, and B is 0.1 Tessla (T) then what is the magnitude of the force?

• F = qvBsin(θ) = qvB

• F = (done on board)

Direction of the force

• But what about the direction the force?

• Is it in the direction of the velocity or the magnetic field?

Direction of the force

• But what about the direction the force?• Is it in the direction of the velocity or the

magnetic field?

• NEITHER! • The force is in the 3rd dimension! • That is the force is perpendicular to both

the velocity and the magnetic field (told you it was complicated).

Right Hand Rule

• To find the direction of the force we use the right hand rule (left hand for a negative charge).

• A = B X C

• A is the thumb.

• B index finger and C is the middle finger

Right Hand Rule

• To find the direction of the force we use the right hand rule (left hand for a negative charge).

• A = B X C (F = q VXB)• A is the thumb.• B index finger and C is the middle finger.

• Lets try one:• The velocity is in the +y direction and the

magnetic field is in the +x direction. • What is the direction of the force?

Okay now lets put it all together!

• A +2C charge is moving in the –y direction at a velocity of 40 m/s.

• If the magnetic field is 0.2 T in the +z direction then what is the magnitude and direction of the force?

One more

• A charge of 3C moving at 5 m/s in the +Z direction experiences a force of 6 N in the –Y direction.

• What is the magnitude and direction of the magnetic field?

Motions in an electric field

• Now that we know what the force is, what will the motion be like if the magnetic field is constant?

• Hint: how does the force change with time as the direction of the velocity of the charge changes?

Motions in an electric field

• Now that we know what the force is, what will the motion be like if the magnetic field is constant?

• The charge will move in a circle!• The force changes the direction of the velocity.• However this changes the direction of the force.• So, the charge will move in a circle

perpendicular to the magnetic field (around the field lines).

• Any motion the particle has in the direction OF the field will be constant (no force).

Cyclotrons

• A device which accelerates particles is called a cyclotron.

• This is used mostly for protons (electrons would just go in the opposite direction).

• This uses the fact that the radius of the circle that a proton will move in just depends on its velocity and the magnetic field.

Centrifugal motion

• Remember in P218 that a = v2/r for circular motions.

• Since a = F/m, then a = qvB / m = v2/r

• So, r = mv / qB and v = qBr / m

• Would do an example, but we are out of time.

Conclusion

• We have learned what magnetic fields are and why they are very important.

• We have learned that the magnitude of the force is qvB and is perpendicular to either v or B.

• We learned how to use the Right Hand Rule to find the direction of the force, velocity, or magnetic field.

• In a constant B field charges move in circles.• We can use this to create a cyclotron.