A charged particle is known as a(n)

The ball will oscillate along the z axis between z=dz=d and z=−dz=−d in simple harmonic motion. What will be the angular frequen

Eddi Din [679]

Answer:

$\omega = \sqrt{\dfrac{kq_0Q}{ma^3} }$

Explanation:

Additional information:

The ball has charge $-q_0$ , and the ring has positive charge $+Q$ distributed uniformly along its circumference.

The electric field at distance $z$ along the z-axis due to the charged ring is

$E_z= \dfrac{kQz}{(z^2+a^2)^{3/2}}.$

Therefore, the force on the ball with charge $-q_0$ is

$F=-q_oE_z$

$F=- \dfrac{kq_0Qz}{(z^2+a^2)^{3/2}}$

and according to Newton's second law

$F=ma=m\dfrac{d^2z}{dz^2}$

substituting $F$ we get:

$- \dfrac{kq_0Qz}{(z^2+a^2)^{3/2}}=m\dfrac{d^2z}{dz^2}$

rearranging we get:

$m\dfrac{d^2z}{dz^2}+ \dfrac{kq_0Qz}{(z^2+a^2)^{3/2}}=0$

Now we use the approximation that

$z^2+a^2\approx a^2$ (we use this approximation instead of the original $d^2+a^2\approx a^2$ since $z$ , our assumption still holds )

and get

$m\dfrac{d^2z}{dz^2}+ \dfrac{kq_0Qz}{(a^2)^{3/2}}=0$

$m\dfrac{d^2z}{dz^2}+ \dfrac{kq_0Qz}{a^{3}}=0$

Now the last equation looks like a Simple Harmonic Equation

$m\dfrac{d^2z}{dz^2}+kz=0$

where

$\omega=\sqrt{ \dfrac{k}{m} }$

is the frequency of oscillation. Applying this to our equation we get:

$m\dfrac{d^2z}{dz^2}+ \dfrac{kq_0Q}{a^{3}}z=0\\\\m=m\\\\k= \dfrac{kq_0Q}{a^{3}}$

$\boxed{\omega = \sqrt{\dfrac{kq_0Q}{ma^3} }}$

5 0

4 years ago

Why do hot-air balloons rise?

natulia [17]

D hope it helps you

7 0

4 years ago

Einstein and Lorentz, being avid tennis players, play a fast-paced game on a court where they stand 20.0 m from each other. Bein

igor_vitrenko [27]

Answer:

A) 185.6 J

B) 9.396 x 10^14 J

C) 4x10^7 m/s

D) 20 m

E) 9.09x10^-8 sec

F) 9.09x10^-8 sec

Explanation:

Detailed explanation and calculation is shown in the image below

3 0

3 years ago

LSE

Zinaida [17]

B) initial speed (u)=3
final speed (v)=8
time (t)= 10
acceleration (a)=?

v=u+at
8=3+a(10)
5=10a
a=1/2= 0.5 m/s²

c)displacement (s)=?
1st section of journey

v ²=u ²+2as
8 ²=3 ²+2(0.5)s
64=9+1s
s=55meters

2nd section of journey
a=0
t=7
u=8
s=?

s=ut+1/2at²
s=8(7)+1/2(0)(7 ²)
s=56 meters

56+55= 111 meters

(For graph x axis =time (sec) & y axis= velocity (m/s))

6 0

3 years ago

What's three pieces of evidence that Wegener used to support his theory ( Alfred Wegener’s hypothesis of continental drift state

Elis [28]

Answer:

In the early part of the 20th century, scientists began to put together evidence that the continents could move around on Earth's surface. The evidence for continental drift included the fit of the continents; the distribution of ancient fossils, rocks, and mountain ranges; and the locations of ancient climatic zones.

6 0

3 years ago