AH 3.1.7 Particles from Space 2

Question 1

What effect does a magnetic field have on a stationary charged particle within the field?

Answer 1

None.

Question 2

What effect does a magnetic field have on a moving charged particle within the field?

Answer 2

The moving charged particle feels a Lorentz force F.

Question 3

Look the the diagram below of an electron moving through a magnetic field of induction B.

Copy the diagram and

a) add the Lorentz force acting on the electron
b) State the equation for the force on the electron
c) What difference would there be if the electron were replaced by a positron (same mass, opposite charge)?

Answer 3

a) The Lorentz Force on the electron acts INTO THE PAGE.
b) F = B q v sinθ
c) The force would be directed in the opposite direction i.e. OUT OF THE PAGE.

Question 4

Copy this diagram and add the force felt by the electron as it enters the magnetic field. Indicate the angle between the electron’s direction of motion and the directions of the force and magnetic induction. State the equation which gives this force.

Answer 4

As the diagram shows, the resulting Lorentz Force is at right angles to the electron’s velocity and at right angles to the magentic induction.

F = Bqv

Question 5

a) Copy this diagram and add the resulting Lorentz Force, F.
b) What is the angle between the Lorentz Force and the electron’s velocity?
c) In such circumstances, what motion will the electron exhibit? Why?
d) Establish a force equation equation and so derive an expression for the radius r.

Answer 5

a) See below.
b) 90^o
c) Uniform circular motion, beacause there is an umbalanced force acting on a body at right angles to it’s uniform velocity vector.
d) Uniform circular motion means there must be a centripetal force F_c = mv²/r

The casue of this centripeal force is the Lorenzt force F_L = B q v = B e v …as the charge is an electron.

So mv²/r = B e v

r = mv² / B e v

r = mv/B e

Question 6

Copy and complete this diagram to show the path of an alpha, beta and gamma as they pass through a magentic field from the bottom of the page and leave it at the top. Assume that the alpha and beta particles anter at the same speed,

Suggest why we do not see complete circular motion exhibted by alpha, beta or gamma here.

Answer 6

See the diagram below.

Gamma has no charge so feels no Lorentz force under any circumstances so is always undeviated. Circular motion is therefore impossoble for gamma here. The gamma ray simply passes starigth through the field undeviated.

Alpha and beta each begin to describe circular motion but the radius of each motion is so large that they do not have time to complete a circle before exiting the magnetic field at the top.

Note that alpha, being MUCH heavier than beta, deflects less i.e. has a much larger radius of curvature.

Question 7

The diagram below shows a particle P describing uniform circular motion in a clockwise direction.

Copy the diagram and indentify clearly

• the magnetic induction B and it’s direction
• the instantaneous velocity v of the particle
• the direction of the Lorentz force F
• the charge on the particle

Answer 7

See below for the completed diagram.

The particle must be positive to be travelling in the circle show - this is found using the Right Hand Motor Rule for ELECTRONS then reversing the force direction to match the required centripetal force direction here.