Particles moving in a circular path

Today we are going to learn

• The formula for the force on a particle in a magnetic field F = B Q v

• Circular path of particles; application in devices such as the cyclotron and Cern

The force on a charged particle in a magnetic field

F = B Q vF = Force (N)B = Magnetic field (T)Q = charge (C)V = velocity (m/s)

when the field is perpendicular to velocity.

Rules for a charged particle in a magnetic field

No work is done by the magnetic field on the particle. The particle only changes direction it does not change its speed.

The charged particle moves in a circular path with the force acting towards the centre of curvature.

If the magnetic field is uniform the particle will travel in a complete circle

Applying a magnetic field

circle if vperpendicularto B

spiral in adissipativemedium

helix if component ofv parallel to B

Fv

B

What will be the radius of the path

Force towards the centre F = BQvCentripetal acceleration a = v2/r Newton’s second law F = ma

BQv = mv2 /r

r = mv/BQ

http://www.vjc.moe.edu.sg/fasttrack/physics/VelocitySelector.htm

r

F = BIL, F = BQV

Q1A wire of length 40cm is placed in a field of 0.15T. The current in the wire is 2.3A.

Calculate the force exerted on the wire. Q2 An electron moving at 200km/s passes at 90o through a magnetic

field of flux density 0.025T. The electron has a charge of -1.6x10-19C and a mass of 9.1x10-31‑kg.

What force is exerted on the electron by the field? What is the radius of the electron’s circular path? (hint: think ‘circular

motion’) Q3 A wire of length 400mm is placed in a field of 1.5x10-1T. The current

in the wire is 2300mA. Calculate the force exerted on the wire.

Q1 A wire of length 40cm is placed in a field of 0.15T. The current in the wire is 2.3A. Calculate the force exerted on the wire. F = Bil (1 mark)F = 0.15 x 2.3 x 0.4 (1 mark)F = 0.14N (1 mark) Q2 An electron moving at 200km/s passes at 90o through a magnetic field of flux density 0.025T. The electron

has a charge of -1.6x10-19C and a mass of 9.1x10-31‑kg. What force is exerted on the electron by the field? F = Bqv (1 mark)F = 0.025 x 1.6x10-19x 200000 (1 mark)F = 8x10-16N (1 mark) What is the radius of the electron’s circular path? (hint: think ‘circular motion’) r = mv2/F (1 mark)r = 9.1x10-31 x (200000)2/ 8 x10-16 or Answer to part a (1 mark)r = 4.9 x 10-5m (1 Mark) Q3 A wire of length 400mm is placed in a field of 1.5x10-1T. The current in the wire is 2300mA. Calculate the force exerted on the wire. F = Bil (1 mark)F = 0.15 x 2.3 x 0.4 (1 mark)F = 0.14N (1 mark)

Cyclotron

http://www.youtube.com/watch?v=M_jIcDOkTAY

The cyclotron is used in hospitals to produce high energy beams of particles.

It consists of 2 D shaped electrodes called the ‘Dees’. The magnetic field is perpendicular and an ac current is applied to the Dees. The AC oscillator creates a potential difference to accelerate the particle. As the particle’s velocity increases its radius will increase until it ready to hit a target.

r = mv/BQ

The Mass SpectrometerMass spectrometers can be used to separate charged particles.

Particles are fired through a slit, and then into a magnetic field. The lightest particles will bend the most, the heaviest will bend the least.

The particles can only get through the slit is they are at the correct velocity as there is a collimator plate creating an electric field before the slit and a magnetic field creating a force on the particle in opposite directions

Cyncatron