 (Parte 8 de 11)

Substitute to obtain: 2 3 kq mTππ==

Motion of Point Charges in Electric Fields

49 • Picture the Problem We can use Newton’s 2nd law of motion to find the acceleration of the electron in the uniform electric field and constant-acceleration equations to find the time required for it to reach a speed of 0.01c and the distance it travels while acquiring this speed.

(a) Use data found at the back of your text to compute e/m for an eme

(b) Apply Newton’s 2nd law to relate the acceleration of the electron to the electric field:

e meEm Fa==net

The Electric Field 1: Discrete Charge Distributions 35 field. electric theopposite iselectron an of onaccelerati theofdirection The

(c) Using the definition of acceleration, relate the time required for an electron to reach 0.01c to its acceleration:

Substitute numerical values and

(d) Find the distance the electron

travels from its average speed and the elapsed time: ()[] () tvx

*50 • Picture the Problem We can use Newton’s 2nd law of motion to find the acceleration of the proton in the uniform electric field and constant-acceleration equations to find the time required for it to reach a speed of 0.01c and the distance it travels while acquiring this speed.

(a) Use data found at the back of your text to compute e/m for an pme

Apply Newton’s 2nd law to relate the acceleration of the electron to the electric field:

p meEm Fa==net

field. electric the ofdirection in the isproton a of onaccelerati theofdirection The

Chapter 21 36

(b) Using the definition of acceleration, relate the time required for an electron to reach 0.01c to its acceleration:

Substitute numerical values and

51 • Picture the Problem The electric force acting on the electron is opposite the direction of the electric field. We can apply Newton’s 2nd law to find the electron’s acceleration and use constant acceleration equations to find how long it takes the electron to travel a given distance and its deflection during this interval of time. (a) Use Newton’s 2nd law to relate the acceleration of the electron first to the net force acting on it and then the electric field in which it finds itself:

e mem

EFa r−==net

Substitute numerical values and evaluate a: r ()

(b) Relate the time to travel a given distance in the x direction to the electron’s speed in the x direction:

xt

(c) Using a constant-acceleration equation, relate the displacement of the electron to its acceleration and the elapsed time:

j ay i.e., the electron is deflected 8.79 cm downward.

52 •• Picture the Problem Because the electric field is uniform, the acceleration of the electron will be constant and we can apply Newton’s 2nd law to find its acceleration and use a constant-acceleration equation to find its speed as it leaves the region in which there is a uniform electric field.

The Electric Field 1: Discrete Charge Distributions 37

equation, relate the speed of the electron as it leaves the region of the electric field to its acceleration and distance of travel:

Apply Newton’s 2nd law to express the acceleration of the electron in terms of the electric field:

e meEm Fa==net

Substitute to obtain:

Remarks: Because this result is approximately 13% of the speed of light, it is only an approximation.

53 •• Picture the Problem We can apply the work-kinetic energy theorem to relate the change in the object’s kinetic energy to the net force acting on it. We can express the net force acting on the charged body in terms of its charge and the electric field.

Using the work-kinetic energy theorem, express the kinetic energy of the object in terms of the net force acting on it and its displacement:

Relate the net force acting on the charged object to the electric field: QEF=net

or, because Ki = 0, xQEK∆=f

Solve for Q:

xE KQ∆=f

Chapter 21 38

Substitute numerical values and

*54 •• Picture the Problem We can use constant-acceleration equations to express the x and y coordinates of the particle in terms of the parameter t and Newton’s 2nd law to express the constant acceleration in terms of the electric field. Eliminating the parameter will yield an equation for y as a function of x, q, and m that we can solve for Ey.

Express the x and y coordinates of the particle as functions of time:

Apply Newton’s 2nd law to relate the acceleration of the particle to the net force acting on it:

mqEm Fayy==ynet,

Substitute in the y-coordinate

sin t m qE tvyy−=θ

Eliminate the parameter t between qE xyyθθ−=

Set y = 0 and solve for Ey:

(Parte 8 de 11)