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storchak [24]
3 years ago
14

If a proton were released from rest at the sphere's surface, what would be its speed far from the sphere?

Physics
2 answers:
balu736 [363]3 years ago
5 0

Let the sphere is having charge Q and radius R

Now if the proton is released from rest

By energy conservation we can say

U = K

\frac{kQe}{R} = \frac{1}{2}mv^2

\frac{2kQe}{mR} = v^2

now take square root of both sides

v =\sqrt{\frac{2kQe}{mR}}

so the proton will move by above speed and

here Q = charge on the sphere

R = radius of sphere

k = 9 * 10^9


il63 [147K]3 years ago
4 0

The speed of proton is about 1 × 10⁷ m/s

<h3>Further explanation</h3>

Electric charge consists of two types namely positive electric charge and negative electric charge.

There was a famous scientist who investigated on this matter. His name was Coulomb and succeeded in formulating a force of attraction or repulsion between two charges.

\large {\boxed {F = k \frac{Q_1 Q_2}{R^2} } }

<em>F = electric force(N)</em>

<em>k = electric constant (N m² / C²)</em>

<em>q = electric charge (C)</em>

<em>r = distance between charges (m)</em>

<em>The value of k in a vacuum = 9 x 10⁹ (N m² / C²)</em>

Let us now tackle the problem!

Let me repeat the question!

<em>A 3.0 cm -diameter isolated metal sphere carries a net charge of 0.90 μC. If a proton were released from rest at the sphere's surface, what would be its speed far from the sphere?</em>

<u>Given:</u>

diameter of sphere = d = 3 cm

charge of sphere = 0.90 μC

mass of proton = 1.67 × 10⁻²⁷ kg

charge of proton = 1.6 × 10⁻¹⁹ C

<u>Unknown:</u>

speed of proton = v = ?

<u>Solution:</u>

We will use the law of conservation of energy to solve this problem.

The potential energy of proton on the surface of the sphere will be the same as the kinetic energy when it is far from the sphere.

Ek = Ep

\frac{1}{2} m_{proton}v^2 = k \frac{Q_{sphere} ~ q_{proton}}{R}

\frac{1}{2} (1.67 \times 10^{-27})v^2 = 9 \times 10^9 \times \frac{0.9 \times 10^{-6} \times 1.6 \times 10^{-19}}{\frac{1}{2} \times 3 \times 10^{-2}}

\large {\boxed {v \approx 1 \times 10^7 ~ m/s} }

<h3>Learn more</h3>
  • The three resistors : brainly.com/question/9503202
  • A series circuit : brainly.com/question/1518810
  • Compare and contrast a series and parallel circuit : brainly.com/question/539204

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Static Electricity

Keywords: Series , Parallel , Measurement , Absolute , Error , Combination , Resistor , Resistance , Ohm , Charge

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Total distance moved by bead is 1.952 cm.

Explanation:

Let first consider all data that are given in question.

1.    F = 8 N                       ...force acting on string

2.   f  = 2 Hz                     ...frequency of system

3.   β = 4 cm = 0.04 m    ...wavelength of wave formed due to vibration           4.   A =  1 cm  = 0.01 m     ...Amplitude of vibration

Under certain conditions, waves can bounce back and forth through a particular region, effectively becoming stationary. These are called standing waves.

Here,it is due to vibration induced in spring due to tension induced in string

Standing wave equation is given by

y = (x,t) = 2A * sinK x * cos (wt)                ...(1)

Let first find, value of K, x, w, t

k = 2 * pi / beta                                          ....(2)

Where β is wavelength in meters

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k = 2 * pi / 0.01

k = 628.31 m^{-1}

now, let us find value of w

W = 2 x pi x f                               ....(3)

                where f is frequency in hertz

W = 2 x pi x 2

W = 4 x pi

W = 0.08 \frac{m}{s}

y = (x,t) = 2A * sinK x * cos (wt)

now, let us find value of v that is wave speed

Notice that some x-positions of the resultant wave are always zero no matter what the phase relationship is.  These positions are called nodes.

Finding the positions where the sine function equals zero provides the positions of the nodes.

In our case, and      

K * x = pi

x = 0.04 / 2

x = 0.02

y = (0.02,1) = 2(0.01) * sin pi  * cos (12.5664 * 1)

y = (0.02,1) = 2(0.01) * -1  * cos 0.9761

Y = 1.952 cm

Finally, when bead is at middle of the string, total distance after stretch covered  is 1.952 cm.

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<h3 />

<h3>What is a resistance thermometer?</h3>

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