Moving charges in a magnetic fieldAQA A-Level Physics: Subtopic test

1. 1
   A beam of protons travels in a vacuum at a speed of 2.0 × 10⁶ m s⁻¹ and enters a region of uniform magnetic field of flux density 0.15 T. The velocity of the protons is at right angles to the field. The charge of a proton is 1.60 × 10⁻¹⁹ C.

   (a)

   What is the magnitude of the force on each proton?

   [1 mark]

   • A4.8 × 10⁻¹⁴ N
   • B2.4 × 10⁻²⁰ N
   • C3.2 × 10⁻¹³ N
   • D8.3 × 10²⁵ N

   (b)

   Which statement correctly describes the effect of the magnetic force on a proton?

   [1 mark]

   • AIts speed increases and its direction is unchanged
   • BIts speed decreases and its direction is unchanged
   • CBoth its speed and its direction change
   • DIts direction changes and its speed stays constant

   (c)

   Explain why the magnetic force does not change the kinetic energy of a proton.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In a vacuum chamber, a beam of protons and then a beam of electrons are fired in turn, each at a speed of 4.0 × 10⁶ m s⁻¹, horizontally due east into a region of uniform magnetic field of flux density 2.0 mT directed vertically upwards. The mass of an electron is 9.11 × 10⁻³¹ kg, the mass of a proton is 1.67 × 10⁻²⁷ kg and the magnitude of the charge on each is 1.60 × 10⁻¹⁹ C.

   (a)

   In which direction is the proton beam deflected as it enters the field?

   [1 mark]

   • ANorth
   • BSouth
   • CEast
   • DVertically downwards

   (b)

   Which statement compares the paths of the electron beam and the proton beam?

   [1 mark]

   • AThe electrons deflect south, on a circle of larger radius than the protons
   • BThe electrons deflect north, on a circle of the same radius as the protons
   • CThe electrons deflect north, on a circle of smaller radius than the protons
   • DThe electrons are not deflected because their mass is very small

   (c)

   Calculate the radius of the circular path of the electrons.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A cyclotron accelerates protons. They move in semicircles inside two hollow, D-shaped metal chambers that lie in a uniform magnetic field of flux density 0.80 T, perpendicular to the plane of the semicircles. Each time a proton crosses the gap between the two chambers it is accelerated by an alternating potential difference. The protons spiral outwards and leave the cyclotron at an outer radius of 0.30 m. Proton mass = 1.67 × 10⁻²⁷ kg and charge = 1.60 × 10⁻¹⁹ C.

   (a)

   Explain why the protons move in semicircles inside the chambers, and why the frequency of the alternating potential difference does not need to change as the protons gain speed.

   [3 marks]

   (b)

   Calculate the maximum kinetic energy of the protons as they leave the cyclotron.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle detector contains a uniform magnetic field of flux density 1.5 T directed vertically upwards. Charged particles fired horizontally into it leave visible tracks that curve in horizontal circles. Looking down from above, one track curves clockwise and another curves anticlockwise. Both tracks spiral inwards as the particles slow down by ionising the liquid in the detector.

   (a)

   Explain how the tracks show the sign of each particle's charge, how the momenta of particles with the same charge can be compared, and why the tracks spiral inwards.

   [6 marks]

   (b)

   One track is an arc of radius 0.042 m made by a positive particle of charge 1.60 × 10⁻¹⁹ C. Calculate the momentum of the particle. Assuming it is a proton of mass 1.67 × 10⁻²⁷ kg, calculate its speed and kinetic energy.

   [6 marks]

   Total for question 4: 12 marks

End of questions