Question

Each of the electrons in the beam of a television tube has a kinetic energy of 17.0 kev. The tube is oriented so that the electrons move horizontally from south to north. The vertical component of Earth's magnetic field points down and has a magnitude of 52.0 μT. (Ignore the northward component of Earth's field.) In what direction will the electron beam deflect? Calculate the acceleration of a single electron due to Earth's magnetic field.

Answer 1

The electron beam will deflect to the west by the Earth's magnetic field. The acceleration of an electron can be calculated using the force experienced in a magnetic field and Newton's second law.

Step-by-step explanation:

The direction of the electron beam will deflect due to the Earth's magnetic field can be determined using the right-hand rule. The electrons are moving from south to north, and the magnetic field is pointing downwards, so the force is directed to the west.

To calculate the acceleration of a single electron due to the Earth's magnetic field, we first need to determine the force acting on the electron. The force (F) experienced by a charged particle moving through a magnetic field is given by the equation F = qv B sin(θ), where q is the charge of the particle, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity of the particle and the magnetic field. For an electron,
`q = -1.6 x 10^-19 C`. The velocity v can be determined from the kinetic energy (KE) using the equation
`KE = 0.5mv^2`, solving for v.

Once the velocity is known, we can find the force, and then the acceleration (a) by using Newton's second law F = ma, and solving for a. Since θ is 90 degrees, sin(θ) equals 1. Dividing the force by the electron's mass gives us the acceleration.