Physics 1102 In-Class Problems: Magnetic Fields

1. An electron travelling with speed v = (5 × 10⁶, 3 × 10⁶, 2 × 10⁶) in a magnetic field B = (0.15, -0.35, 0.50). Find the magnetic force exerted on the electron.
   

2. In the diagrams below, draw or indicate the direction of the magnetic force on the moving charge and calculate its magnitude.

   (a) q = +5.0 μC, v = 15.0 × 10³ m/s, B = 0.25 T, θ = 65°

   

   (b) q = -3.0 μC, v = 6.0 × 10³ m/s, B = 0.25 T, θ = 122°

   

   (c) q = +5.0 μC, v = 15.0 × 10³ m/s, B = 0.25 T

   

   (d) q = -5.0 μC, v = 15.0 × 10³ m/s, B = 0.25 T

   

   (e) q = +5.0 μC, v = 15.0 × 10³ m/s, B = 0.25 T

   

   (f) q = -5.0 μC, v = 15.0 x × 10³ m/s, B = 0.25 T

   

3. An electron is travelling through a uniform magnetic field of magnitude B = 1.5 × 10^-3 T directed as in the diagram below. With what speed and direction must the electron be moving such that the magnetic force exactly balances the force due to gravity? The charge of an electron is -1.60 × 10^-19 C and its mass is 9.11 × 10^-31 kg.
   
   

4. A electric power line carries a current of 1400 A in a location where the earth's magnetic field is 5.0 × 10^-5 T. The line makes an angle of 75° with respect to the field. Determine the magnitude of the magnetic force on a 120-m length of line.

   The earth's magnetic field is approximately 5 × 10^-5 T. If an electron is travelling perpendicular to the field at 1000 m/s, determine its cyclotron radius and frequency. Ignore the effects of gravity and the electric field of the atmosphere. The mass of an electron is 9.11 × 10^-31 kg.
   

5. A beam of protons moves in a circle of radius 0.25 m. The beam moves perpendicular to a 0.30 T magnetic field. (a) What is the speed of each proton? (b) Determine the cyclotron frequency of the protons. (c) Determine the magnitude of the centripetal force on each proton. Protons have mass 1.673 × 10^-27 kg.
   

6. A velocity selector with an electric field of 4.50 × 10³ V/m and a magnetic field of 0.100 T is used to select the speed of an ion of charge +e before it enters a mass spectrometer. A 0.400-T magnetic field then bends the ion into a circular path of radius 0.230 m. What is the mass of the ion? What is the atomic mass of the ion? What element is the ion? (Atomic mass is the mass in grams of one mole of the substance. N_A = 6.022 × 10²³)

7. Suppose that an ion source produces doubly ionized gold ions (Au++), each with a mass of 3.27 × 10^-25 kg. The ions are passed through a velocity selector with E = 5.00 × 10³ V/m and B = 0.150 T. Then, a 0.500-T magnetic field causes the ions to follow a circular path. Determine the radius of the path.
   

8. In the Bohr model of the hydrogen atom, an electron in the ground state has a speed of 2.20 × 10⁶ m/s at a radius of 5.29 × 10^-11 m. The charge of an electron is 1.60 × 10^-19 C. Find the magnetic dipole moment of the atom.
   

Questions? mike.coombes@kpu.ca