Magnetic Force on Moving Charges

Magnetic Force on Moving Charges

• Moving electrons produce a magnetic force, so a magnetic force can produce moving electrons.

• This principle explains– Aurora borealis (aurora australis)– Animal navigation– Television sets (old-school)– Particle accelerators, CERN

Magnetic Force on a Charge

• The force of a magnetic field (FM)on a charged object depends on:

– The amount of charge on the object (q)– The strength of the magnetic field (B)– The velocity the object is moving (v)– The angle between the velocity and the

magnetic field (Ɵ)

B

q

v

In most cases, Ɵ will be 0o or 90o.

Magnetic Force

sinqvBFM

Magnetic Force (N)

Charge moving (C)

Velocity of Charge (m/s)

Magnetic Field Strength (Tesla)1 T = 1 kg/C.s

Angle between B and v

Direction of FM

RHR for q in a B Field

v

Magnetic Force on a Conductor

• Charged particles moving through a conductor cannot leave the conductor.

• The force they experience is transferred to the conductor as a whole.

• If we think of the current (I) in the conductor as a flow of charges (q) moving at a velocity (v) over a distance (L), the force equation becomes:

sinIlBFM

Magnetic Force (N)

Current (A)

Length of Wire (m)

Magnetic Field Strength (Tesla)1 T = 1 kg/C.s

Angle between B and I

Direction of FM

RHR for q in a B Field

I

Particle Accelerators

• Particle accelerators falls into one of two categories– Circular (synchrotron)– Linear.

Simple Principle

• A particle accelerator experiment has been described as determining the structure of a television by looking at the pieces after it has been dropped from the Empire State Building.

Original Accelerators

Developed by Ernest O. Lawrence in 1929

• Particle motion is isochronous (time taken is the same as speed increases)

• Max energy 1x10-12 J– Relativistic Effects

Modern Accelerators

• Modern circular accelerators place electromagnets around a circular copper tube to keep the particle beam focused.

Modern Accelerators

• Modern circular accelerators use Klystrons (which produce microwaves) to accelerate the particles.

• The copper tube of the accelerator is arranged to form a series of cavities. The spacing of the cavities is matched to the wavelength of the microwaves.

• Circular accelerators propel particles around a circular track many times. At each pass, the magnetic field is strengthened so that the particle beam accelerates with each consecutive pass

Recommended Problems

• Pg. 396 #2-5• Pg. 405 #1, 2, 4