# Magnetic Fields

1 Tesla is a very strong magnetic field

More common non-SI units is the Gauss

Earth's magnetic field strength ≈ 0.5 Gauss

# Forces on Moving Charges

The magnetic force is always perpendicular to the charged object's velocity, therefore the magnetic force on a moving charge is never applied in the direction of the displacement, therefore a magnetic force can do no work on a moving charge (but it can change its direction)

# Direction of the Magnetic Force

Direction of the force given by right-hand rule

Point fingers of right hand in direction of positive particles' velocity

Curl fingers inward in the direction of the magnetic field

Thumb points in the direction of the force on charged particle

# Path of Charged Particles in B Fields

Magnetic force cannot perform work on a moving charge

Magnetic force can change its direction (moving it in a circle if the magnetic force is constant)

# Total Force on a Moving Charged Particle

E field can do work on a moving charge

B filed can never do work on a moving charge

Lorentz Force

# Velocity Selector

A charged particle in crossed E and B fields can undergo constant velocity motion is v, B, and E are all selected perpendicular to each other

# Mass Spectrometer

Magnetic fields accelerate moving charges so that they travel in a circle

This can be used to determine the mass of an unknown particle!

# Example 1: Velocity Selector

Find the speed of a charged particle which passes through a velocity selector with magnetic field strength of 1 Tesla perpendicular to an electric field of 600,000 N/C

# Example 2: Mass Spectrometer

- A proton is accelerated through a potential difference V before passing into a region of uniform magnetic field B as shown

Determine the voltage necessary to give the proton a speed v as it enters the magnetic field region in terms of the proton's mass m, its velocity v, and its charge,

`q.`

Determine an expression for the radius of the proton's motion in the uniform magnetic field

`region`

Sketch the path of the proton in the magnetic field

An electric field is applied in the same region as the uniform magnetic field. Determine the magnitude and direction of electric field required so that the proton passes through the region in a straight line