An electron in the beam of a TV picture tube is accelerated...

An electron in the beam of a TV picture tube is accelerated by a potential difference of 2.00 $\mathrm{kV}$ . Then it passes through a region of transverse magnetic field, where it moves in a circular arc with radius 0.180 $\mathrm{m} .$ What is the magnitude of the field?

Key Concepts

Centripetal Force and Circular Motion

When a charged particle moves in a magnetic field and experiences a Lorentz force that is perpendicular to its velocity, it undergoes circular motion. In this context, the magnetic force provides the necessary centripetal force to keep the particle moving in a circular path. The relation qvB = mv^2/r, where m is the mass and r is the radius of the circular path, links the magnetic field strength to the curvature of the particle's trajectory.

Relationship between Electric Acceleration and Magnetic Deflection

By combining the energy conversion equation, which gives the velocity of the particle after acceleration (derived from v = sqrt(2q?V/m)), with the centripetal motion formula, it is possible to determine the magnetic field strength that causes the observed circular deflection. This integration of concepts is key in problems where charged particles are first accelerated by an electric field and then deflected by a magnetic field.

Electric Potential Energy and Kinetic Energy Conversion

When a charged particle, such as an electron, is accelerated through a potential difference, its electric potential energy is converted into kinetic energy. This conversion is described by the equation K = q?V, where K is the kinetic energy, q is the charge of the particle, and ?V is the potential difference. This concept is fundamental in understanding how particles gain speed in devices like cathode-ray tubes.

Lorentz Force on a Moving Charge

A moving charged particle in a magnetic field experiences the Lorentz force, which is given by F = qvB sin?. When the magnetic field is perpendicular to the velocity of the particle, as is often the case in controlled experiments, the sin? term becomes 1. This force is responsible for deflecting the particle's path, and is directly proportional to the charge, the particle's speed, and the strength of the magnetic field.

Transcript

Please give Ace some feedback