A beam of electrons traveling with a speed of 3.0 ×10^7 m / s enters a uniform, downward electri

step 1 a beam of electrons traveling it is a speed of 3 into 4 7 meter per second so the speed v is at

A beam of electrons traveling with a speed of 3.0 ×10^7 m /...

A beam of electrons traveling with a speed of $3.0 \times$ $10^{7} \mathrm{m} / \mathrm{s}$ enters a uniform, downward electric field of magnitude $2.0 \times 10^{4} \mathrm{N} / \mathrm{C}$ between the deflection plates of an oscilloscovpe. The initial velocity of the electrons is perpendicular to the field. The plates are $6.0 \mathrm{cm}$ long. (a) What is the direction and magnitude of the change in velocity of the electrons while they are between the plates? (b) How far are the electrons deflected in the \pmy-direction while between the plates?

A beam of electrons traveling with a speed of $3.0 \times$ $10^{7} \mathrm{m} / \mathrm{s}$ enters a uniform, downward electric field of magnitude $2.0 \times 10^{4} \mathrm{N} / \mathrm{C}$ between the deflection plates of an oscilloscovpe. The initial velocity of the electrons is perpendicular to the field. The plates are $6.0 \mathrm{cm}$ long.
(a) What is the direction and magnitude of the change in velocity of the electrons while they are between the plates?
(b) How far are the electrons deflected in the \pmy-direction while between the plates?

Key Concepts

Uniform Electric Field

A uniform electric field is one in which the strength and direction are constant at every point. This concept is important because it allows for a constant force on a charged particle, which simplifies the analysis of its motion. When electrons enter such a field, they experience a constant acceleration in the direction of the force due to the field, regardless of their initial velocity direction (if it is perpendicular).

Electric Force on Charged Particles

Charged particles in an electric field experience an electric force, given by the equation F = qE, where q is the charge of the particle and E is the electric field strength. The direction of the force depends on the sign of the charge. For electrons, which have a negative charge, the force is opposite to the direction of the electric field, a key factor when determining the trajectory and deflection.

Newton's Second Law

Newton's Second Law, stated as F = ma, connects the net force acting on an object to the acceleration it experiences. This law is crucial when analyzing the motion of electrons in an electric field because it allows us to calculate the acceleration (a) by dividing the electric force (F) by the electron's mass (m).

Kinematics with Constant Acceleration

The equations of kinematics describe the motion of particles under constant acceleration. Once the acceleration of the electrons is determined, these equations can be applied to calculate changes in velocity and displacement over time. In problems like these, the time of flight through the field is determined by the length of the electric field region and the initial horizontal velocity.

Time of Flight and Perpendicular Motion

The time the electrons spend between the plates is calculated based on their constant horizontal velocity and the length of the deflection plates. This time interval is then used to compute the change in vertical velocity and the vertical displacement (deflection) due to the constant acceleration caused by the electric field.

Transcript

Please give Ace some feedback