Question

The electrons in the beam of a television tube have an energy of 12 keV. The tube is oriented so that the electrons move horizontally from east to west. The vertical component of the Earth's magnetic field at the location of the television has a magnitude of 53.0

T and is pointing down.

a) In which direction does the force on the electrons act? Neglect a possible horizontal component of the magnetic field.

b) What is the magnitude of the acceleration due to the vertical component of the Earth's magnetic field of an electron in the beam?

c) If the inclination of the earth's magnetic field near the TV is 10 degrees, calculate the magnitude of the force on the electrons due to the horizontal component of the Earth's magnetic field.

Answer 1

The force on the electrons acts in the northward direction. The magnitude of the acceleration due to the vertical component of the Earth's magnetic field can be calculated using the formula a = qvB/m. The magnitude of the force on the electrons due to the horizontal component of the Earth's magnetic field can be calculated using the formula F = qvBsin(theta).

Step-by-step explanation:

When electrons move horizontally from east to west in a television tube, the magnetic force on the electrons acts perpendicular to the direction of their motion and also perpendicular to the magnetic field. In this case, since the vertical component of the Earth's magnetic field is pointing down, the force on the electrons will be in the northward direction.

The magnitude of the acceleration due to the vertical component of the Earth's magnetic field can be calculated using the formula a = qvB/m, where q is the charge of the electron, v is the velocity of the electron, B is the magnitude of the magnetic field, and m is the mass of the electron. By plugging in the given values and using the appropriate SI units, you can calculate the magnitude of the acceleration.

To calculate the magnitude of the force on the electrons due to the horizontal component of the Earth's magnetic field, you can use the formula F = qvBsin(theta), where theta is the angle of inclination of the Earth's magnetic field. By plugging in the given values and using the appropriate SI units, you can calculate the magnitude of the force.