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

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 oscilloscope. 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 $\pm$ y-direction while between the plates? CAN'T COPY THE FIGURE

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 oscilloscope. 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
$\pm$ y-direction while between the plates?
CAN'T COPY THE FIGURE

Key Concepts

Time of Flight and Displacement

This concept involves determining the time the particle spends within a region (like between deflection plates) based on its horizontal velocity and the length of the region, and then using that time to predict vertical displacement with the equation y = 0.5at², where a is the acceleration and t is the time interval.

Projectile Motion in Two Dimensions

This principle treats the motion of the charged particle as two independent components - horizontal motion with constant velocity and vertical motion with constant acceleration. Even when the particle is accelerated vertically by the electric force, its horizontal velocity remains constant, allowing for separate analysis of each component of motion.

Electric Force on a Charged Particle

This concept explains that a charged particle, like an electron, experiences a force when placed in an electric field. The magnitude and direction of the force are given by F = qE, where q is the charge of the particle and E is the electric field strength. The sign of the charge determines whether the force is in the same or opposite direction to the field.

Acceleration Due to the Electric Field

This involves applying Newton's second law, F = ma, to find the acceleration of the charged particle under the influence of the electric force. By rearranging the equation to a = F/m, one can calculate the constant acceleration imparted to the particle during its time within the electric field.

Transcript

00:01 This problem has electrons being shot between two charged plates with a uniform electric field between them.

00:06 The first part of this problem wants you to figure out what the change in velocity, both direction and magnitude, is of the electrons, once they come out of the plates.

00:13 So figuring out the time that they're between the plates is real easy.

00:16 You just take the distance that they're traveling in the plates, six centimeters, and then divide that by their speed, their horizontal speed, which is three times 10 to the seventh meters per second.

00:29 That comes out to 2 nanoseconds.

00:35 We also need the force so that we can find the acceleration on the electrons.

00:42 As you know, force is the charge times the electric field when it comes to charged particles.

00:48 In this problem, e is our charge because that's the charge of an electron.

00:52 And our electric field is given as 2 times 10 to the 4th.

00:58 This comes out to 3 .2 times 10 to the negative 15th newton's.

01:07 Furing out acceleration from this is pretty simple.

01:09 A is f over m by newton's second law.

01:16 We just found force.

01:18 M is the mass of an electron.

01:25 I'm just going to write m .e.

01:27 And so our acceleration is 3 .52 times 10 to the 15th meters per second squared...

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