Permeability of free space: m0 = 4p × 10-7 Hm-1

PSC 32: Magnetic Fields 2

Permeability of free space: m₀ = 4p × 10^-7 Hm^-1

Charge of electron: e = -1.60 × 10^-19 C

For purposes of this PSC: 1 u ≈ mass of proton ≈ mass of neutron ≈ 1.67 x 10^-27 kg

1. A proton is in a circular orbit of radius 20.0 cm perpendicular to a 0.800 T field. Find: (a) its speed; (b) its period; (c) its kinetic energy.

2. A proton moving freely in a circular path perpendicular to a constant magnetic field takes 1.00 ms to complete one revolution. Determine the magnitude of the magnetic field.

3. In a certain experiment protons and alpha particles must move with the same radius normal to a magnetic field whose strength can be changed. Find the ratio of the field strengths needed if they have the same value for the following: (a) speed; (b) linear momentum; (c) kinetic energy.

4. Consider the mass spectrometer shown schematically in the figure. The electric field between the plates of the velocity selector is 9950 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.930 T. Calculate the radius of the path in the system for a singly charged ion with mass m = 2.18 × 10^-26 kg.

Note: Charged particles are first sent through a velocity selector. They then enter a region where a magnetic field B₀ (directed inward) causes positive ions to move in a semicircular path and strike a photographic film at P.

5. A mass spectrometer is used to examine the isotopes of uranium. Ions in the beam emerge from the velocity selector at a speed of 3.00 × 10⁵ m/s and enter a uniform magnetic field of 0.600 T directed perpendicular to the velocity of the ions. What is the distance between the impact points formed on the photographic plate by singly charged ions of ²³⁵U and ²³⁸U?

6. Consider a charged particle moving with velocity v in a uniform magnetic field such that the charged particle is NOT moving perpendicular to the magnetic field (also, not in the same direction as the magnetic field). Such a charged particle moves in a helical path. The “pitch” of the helix is the displacement of the particle in the direction of the path in one period.

a. Determine an expression for the “pitch”.

b. An electron moving at 4.00 × 10⁶ m/s enters a uniform field B = 0.0400 T at 30° to the lines. What is the pitch of the helical path?

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