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3 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]3 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

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3 years ago

A monkey running through the jungle goes 0.198 km straight to the East, then turns 15.8° deflection from straight East toward th

inn [45]

Answer:

$|\vec r|=339.82\ m$

$\theta=-6.67^o$

Explanation:

<u>Displacement </u>

It's a vector magnitude that measures the space traveled by a particle between an initial and a final position. The total displacement can be obtained by adding the vectors of each individual displacement. In the case of two displacements:

$\vec r=\vec r_1+\vec r_2$

Given a vector as its polar coordinates (r,\theta), the corresponding rectangular coordinates are computed with

$x=rcos\theta$

$y=rsin\theta$

And the vector is expressed as

$\vec z==$

The monkey first makes a displacement given by (0.198 km,0°). The angle is 0 because it goes to the East, the zero-reference for angles. Thus the first displacement is

$\vec r_1==\ km=\ m$

The second move is (145 m , -15.8°). The angle is negative because it points South of East. The second displacement is

$\vec r_2==\ m$

The total displacement is

$\vec r=\ m+\ m$

$\vec r=\ m$

In (magnitude,angle) form:

$|\vec r|=\sqrt{337.52^2+(-39.48)^2}=339.82\ m$

$\boxed{|\vec r|=339.82\ m}$

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3 years ago

When driving at night, only use your high-beam headlights___

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Answer:

B

Explanation:

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2 years ago

A box is held at rest by two ropes that form 30° angles with the vertical. The tension T in either rope is 42 N. What is the wei

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<h3><u>Answer;</u></h3>

= 73 N

<h3><u>Explanation</u>;</h3>

Using the formula

2 T cos(30°) = w

Where; T is the tension on each string, while w is the weight of the box given by mg

Therefore;

W = 2Tcos 30°

= 2 × 42 cos 30°

= 84 cos 30°

= 72.74

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3 years ago

One of the fastest recorded pitches major-league baseball, thrown by nolan ryan in 1974, was clocked at 100.8 mi/hr. If a pitch

lawyer [7]

<u>Answer:</u>

The ball fall vertically 2.69 ft by the time it reached home plate 60.0 ft away.

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We have the horizontal velocity = 44.8 m/s

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The distance traveled by baseball vertically is found out by equation $s=ut+\frac{1}{2} at^2$

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Substituting

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So vertical distance traveled = 0.82 m = 2.69 ft

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2 years ago

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