Ask question

Ask question

All categories

4 years ago

5

An electric charge q of mass m in an oscillating electric field Eosinot experiences force q Eosinot. Suppose it starts from rest

at time to, and position x-0. a) What is its velocity as a function of time? b) What is its kinetic energy as a function of time? c) What is the particle's time averaged kinetic energy (averaged over an integer # of complete cycles)? d) The vector potential A is defined so that the electric field is E at and the canonical momentum is then given by Pcan P can (t). mv + qA. Find A(t) and

1 answer:

Masja [62]4 years ago

7 0

Answer:

speed of the charge electric is v = - (Eo q/m) cos t

Explanation:

The electric charge has a very small mass so it follows the oscillations of the electric field. We force ourselves on the load,

F = q Eo sint

a) To find the velocity of the particle, let's use Newton's second law to find the acceleration and of this by integration the velocity

F = ma

q Eo sint = ma

a = Eo q / m sint

a = dv / dt

dv = adt

∫ dv = ∫ a dt

v-vo = I (Eoq / m) sin t dt

v- vo = Eo q / m (-cos t)

We evaluate the integral from the initial point, as the particle starts from rest Vo = 0, for t = 0

v = - (Eo q / m) cos t

b) Kinetic energy

K = ½ m v2

K = ½ m (Eoq / m)²2 (sint)²

K = ¹/₂ Eo² q² / m sin² t

c) The average kinetic energy over a period

K = ½ m v2

<v2> = (Eoq / m) 2 <cos2 t>

The average of cos2 t = ½, substitute and calculate

K = ½ m (Eoq / m)² ½

K = ¼ Eo² q² / m

You might be interested in

W is the work done on the system, and K, U, and Eth are the kinetic, potential, and thermal energies of the system, respectively

MArishka [77]

Answer:

1) a block going down a slope

2) a) W = ΔU + ΔK + ΔE, b) W = ΔE, c) W = ΔK, d) ΔU = ΔK

Explanation:

In this exercise you are asked to give an example of various types of systems

1) a system where work is transformed into internal energy is a system with friction, for example a block going down a slope in this case work is done during the descent, which is transformed in part kinetic energy, in part power energy and partly internal energy that is represented by an increase in the temperature of the block.

2)

a) rolling a ball uphill

In this case we have an increase in potential energy, if there is a change in speed, the kinetic energy also increases, if the change in speed is zero, there is no change in kinetic energy and there is a change in internal energy due to the stationary rec in the point of contact

W = ΔU + ΔK + ΔE

b) in this system work is transformed into internal energy

W = ΔE

c) There is no friction here, therefore the work is transformed into kinetic energy

W = ΔK

d) if you assume that there is no friction with the air, the potential energy is transformed into kinetic energy

ΔU = ΔK

7 0

3 years ago

Water waves, earthquake waves, sound waves, and the waves that travel down a rope or spring are all examples of what waves.

Margaret [11]

Compression waves :-)

5 0

3 years ago

Determine the volume displaced and then calculate the density of this 54 g sample of brass.

inessss [21]

Answer:

DETAILS IN THE QUESTION INSUFFICIENT TO ANSWER

Explanation:

Assuming the liquid to be water ,

the density $d_{w}$ of water is : $1000kgm^{-3}=1gcm^{-3}$

Buoyant force exerted by a liquid on an object with $V_{imm}$ of it's volume immersed is :

$F_{B}=V_{imm}*d_{l}*g$

where ,

$F_{B}$ is the buoyant force
$d_{l}$ is the density of the liquid
$g$ is the acceleration due to gravity

Thus at equilibrium:

$m_{brass}*g=V_{imm}*d_{l}*g\\m_{brass}=V_{imm}*d_{l}\\54=V_{imm}*1\\V_{imm}=54cm^{3}$

from these , we get the density of brass to be $1gcm^{-3}$

which is not possible

7 0

3 years ago

If you were doing a research study on sleep and student achievement, which

jasenka [17]

Letter D: The amount of sleep a student gets affects student achievement

6 0

3 years ago

Read 2 more answers

Carpet can keep a room quiet by:

taurus [48]

Hard surfaces reflect sound back into the room, while carpets help to absorb the sound so it reflects less

6 0

3 years ago