SP212 Lesson 18Ch. 28, 1 – Magnetic Fields

February 15, 2018

SP212 Lesson 18 February 15, 2018 1 / 7

Aside: Electron Guns

Use the E-field to make a beam of electrons!

1 Run a current through a heated cathode (-) to“loosen” the electrons’ binding to the wire.

2 Use the electric field of the Anode (+) to acceleratethe beam through a gap in the anode. E fieldcreates “Accelerating Voltage” Vb

3 The Wehnelt Cylinder is also negative to “collimate”(align) the beam.

4 The field does W=qVb work on the electrons.

5 Electrons now have kinetic energy! K = 12mv2

6 12mv2 = qVb so v =

√2qVb

m

7 Vb=5000 V gives v = 4.2× 107 m/s

SP212 Lesson 18 February 15, 2018 2 / 7

The Magnetic Field (~B)

Humans have long known about magnetism.Lodestones – natural magnets.Compasses – navigation.

We used them, but didn’t understand them!

The breakthrough in understanding came by understanding that magnetism wasanother field, similar to Electrostatics. It affects MOVING changes (and thatimplies that ferromagnetic materials are composed of moving charge).

Recall our original definition of the electric field E:

~FE = ~Eq

Our new magnetic field has a similar (though not quite as simple) equation:

~FB = q~v × ~BFB = |q|vB sinφ

SP212 Lesson 18 February 15, 2018 3 / 7

Magnetic Field Lines

Magnetic fields, like electric fields, can be drawn using magnetic field lines.Magnetic field lines always start on north poles and end on south poles.

All magnets have these two poles. There are ONLY magnetic dipoles.

Similarly to electric charges, like magnetic poles repel, opposite poles attract!

SP212 Lesson 18 February 15, 2018 4 / 7

The Magnetic Field

Based on its formula, the unit for the magnetic field is the tesla (T):

1 T = 1 N A−1 m−1

Sometimes you will still see magnetic field measured in gauss (G):

1 G = 1× 10−4 T

The earth’s magnetic field is about 1 G at the surface.

SP212 Lesson 18 February 15, 2018 5 / 7

Details, details, details....

It’s never simple. ~FB = q~v × ~B has properties.

The force requires the charge have a relative motion. No motion? No force.

The force is at right angles to the field and velocity. We need cross products andthe right hand rule! Here, a is ~v, b is ~B and aXb is ~FB

We will draw lots of 3-d spaces. A vector into the boardis the cross, out of the board is a dot.

A negative charge REVERSES the direction of ~Fb!!!!

SP212 Lesson 18 February 15, 2018 6 / 7

RHR Challenge....

The figure shows three situations in which a positively charged particle moveswith velocity ~v through a uniform magnetic field ~B and experiences a magneticforce ~FB as a result.

For each situation, determine whether the orientation of the vectors are physicallyreasonable.

SP212 Lesson 18 February 15, 2018 7 / 7