Estimate the approximate maximum deflection of the elec-...

Estimate the approximate maximum deflection of the elec- tron beam near the center of a CRT television screen due to the Earth's $5.0 \times 10^{-5}$ Tield. Assume the screen is 18 $\mathrm{cm}$ from the electron gun, where the electrons are accelerated (a) by 2.0 $\mathrm{kV}$ , or $(b)$ by 28 $\mathrm{kV}$ . Note that in color TV sets, the beam must be directed accurately to within less than 1 $\mathrm{mm}$ in order to strike the correct phosphor. Because the Earth's field is significant here, mu-metal shields are used to reduce the Earth's field in the CRT.

Estimate the approximate maximum deflection of the elec-
tron beam near the center of a CRT television screen due to
the Earth's $5.0 \times 10^{-5}$ Tield. Assume the screen is 18 $\mathrm{cm}$
from the electron gun, where the electrons are accelerated (a) by 2.0 $\mathrm{kV}$ , or $(b)$ by 28 $\mathrm{kV}$ . Note that in color TV sets, the
beam must be directed accurately to within less than 1 $\mathrm{mm}$
in order to strike the correct phosphor. Because the Earth's
field is significant here, mu-metal shields are used to reduce
the Earth's field in the CRT.

Key Concepts

Magnetic Deflection and Trajectory Estimation

Deflection of a charged particle results from its curved trajectory in a magnetic field. By relating the parameters of circular motion to the geometry of the system, one can estimate the maximum displacement from an initial straight-line path. This concept is used to predict how external magnetic fields can affect the position of an electron beam or similar charged particle streams.

Circular Motion of Charged Particles in a Magnetic Field

Once in a uniform magnetic field, a charged particle undergoes circular motion due to the constant perpendicular force provided by the Lorentz force. The radius of this circular path, given by r = mv/(qB), is determined by the particle's mass, velocity, charge, and the strength of the magnetic field.

Lorentz Force

This is the fundamental force experienced by a charged particle moving in a magnetic field, expressed by the equation F = q(v × B). It is the basis for understanding how magnetic fields influence the motion of electrons and other charged particles, causing them to follow curved trajectories rather than straight lines.

Potential Difference and Electron Acceleration

When electrons are accelerated by a potential difference, they convert electrical potential energy into kinetic energy. The relationship eV = (1/2)mv² allows us to determine the velocity of the electrons after acceleration, which is crucial for calculating their subsequent motion in a magnetic field.

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