An infinitely long line of charge has a linear charge density of 8.00*10^−12 C/m. A proton is at distance 19.0 cm from the line and is moving directly toward the line with speed 1200 m/s. How close does the proton get to the line of charge?

Answers

Answer 1

Hi there!

To solve, we need to find the distance traveled by the proton at which the proton's velocity reaches 0 m/s. This indicates the point at which the repulsive force caused by the line of charge and its consequential acceleration causes the proton to stop for an instant and be repelled back in the opposite direction.

For this, we can use the work-energy theorem to solve.

Recall the following equations:
[tex]W = \Delta KE[/tex]

[tex]W = \int F \cdot dx\\\\KE = \frac{1}{2}mv^2[/tex]

We will integrate along the path from the point 19.0 cm (0.19 m) from the line up to a point 'z' at which the proton has no kinetic energy (v = 0 m/s). This means that the wire will be doing NEGATIVE work on the proton as it is decreasing the proton's kinetic energy.

The equation for a force acting on a charged particle is given as:
[tex]F_E = qE[/tex]

For an infinite line of charge, the electric field is given as:
[tex]E = \frac{2k\lambda}{r}\\\\F_E = \frac{2k\lambda q}{r}[/tex]

**λ = Linear charge density (C/m)

To set up our integral:
[tex]W = \Delta KE = \int\limits^z_{0.19} {\frac{2k\lambda q}{r}} \, dr = -\frac{1}{2}mv^2[/tex]

Integrate using the following natural log rule:
[tex]\int {\frac{1}{r}} \, dr = ln(r) + C[/tex]

[tex]\int\limits^z_{0.19} {\frac{2k\lambda q}{r}} \, dr = -\frac{1}{2}mv^2\\\\2k\lambda q ln(r) \left \| {{z} \atop {0.19}} \right. = -\frac{1}{2}mv^2\\\\2k\lambda q (ln(z) - ln(0.19) = -\frac{1}{2}mv^2\\\\2k\lambda q ln(\frac{z}{0.19}) = -\frac{1}{2}mv^2[/tex]

Now, we can begin solving for 'a'.

Move coefficients to one side:
[tex]ln(\frac{z}{0.19}) = -\frac{mv^2}{4k\lambda q }[/tex]

Take the base 'e' of both sides:
[tex]e^{ln(\frac{z}{0.19})} = e^{-\frac{mv^2}{4k\lambda q }}\\\\\frac{z}{0.19} = e^{-\frac{mv^2}{4k\lambda q }}\\\\z = (0.19)e^{-\frac{mv^2}{4k\lambda q }}\\\\z = (0.19)e^{-\frac{(1.67*10^{-27})(1200^2)}{4(8.99*10^9)(8.00*10^{-12}) (1.6*10^{-19}) }}\\\\\boxed{z = 0.1803 m= 18.03 cm}[/tex]

It will reach a distance 18.03 cm from the wire before it temporarily loses all of its kinetic energy (at rest) and begins to speed up in the opposite direction.


Related Questions

A 425-g piece of metal at 100°C is dropped into a 100-g aluminum cup containing 500 g of water at 15°C. The final temperature of the system is 40°C. What is the specific heat of the metal, assuming no heat is exchanged with the surroundings? The specific heat of aluminum is 900 J/kg°C.

a. 2140 J/(kg•K)
b. 3800 J/(kg•K)
c. 3300 J/(kg•K)
d. 1900 J/(kg•K)
e. 4280 J/(kg•K)

Answers

The specific heat of the metal, assuming no heat is exchanged with the surroundings is 2140 J/(kg•K).

Specific heat capacity of the metal

The specific heat capacity of the metal is determined from the principle of conservation of energy.

energy lost by the metal = energy gained by aluminum + energy gained by water

Q = mcΔθ

where;

m is mass (kg)c is specific heat capacityΔθ is change in temperature

0.425c(100 - 40) = 0.1(900)(40 - 15) + 0.5(4186)(40 - 15)

25.5c = 2250 + 52,325

c = 54,575/25.5

c = 2140 J/(kg•K)

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What is the acceleration of a car that goes from 22.0 km/h to 64.0 km/h in 9.4 seconds? (Answer to 1 decimal place)

Answers

22.0 km/h = 6.11 m/s
64 km/h = 17.8 m/s
a = (v(final) - v(initial))/time
a = (17.8 - 6.11)/9.4
a = 1.23 m/s = 4.43 km/h

PLEASE HELP a current of 0.5 A flows with a resistance of 50 ohms what is the e.m.f applied NEED HELP ASAP AND BRAINLIEST​

Answers

Answer:

25 volts

Explanation:

voltage = current × resistance

[tex]v = i \times r \\ v = 0.5 \times 50 \\ v = 25v[/tex]

The rubber band contains .......potential energy as it is stretched.

less

more

same

Answers

Answer:

elastic potential energy

You input potential (stored) energy into the rubber band system when you stretched the rubber band back. Because it is an elastic system, this kind of potential energy is specifically called elastic potential energy.

Explanation:

You are on a boat in the middle of the Pacific Ocean at the equator traveling in a hydrofoil
going at a constant speed of 300 /. The water is perfectly still. What is your acceleration:
a) If you’re heading due North?
b) If you’re heading due East?
c) If you’re heading straight up (something probably went wrong at this point).
You may assume the following:
The earth has a radius of 6371 km.
The earth makes one full revolution every 24 hours.
The gravitational constant at sea level is 9.81 m/s2
East and North are relative to the Earth’s axial north, not magnetic north.

Answers

a) If you’re heading due North, total acceleration will be 0.0478 m/s².

b) If you’re heading due East, acceleration will be 0.0803 m/s².

c) If you’re heading straight up, no exact value for acceleration.

What is acceleration?

The time rate of change of velocity is known as acceleration.

a)If the boat is going along North from equator, there will be only centrifugal force acting along upward direction which will be balanced by the weight of boat.

Angular velocity ω= (2π / (3600 x 24)) = 7.27 x 10⁻⁵ rad/s

Acceleration due to centrifugal force a = 0.0337m/s²

Centrifugal force due to its own velocity 300 m/s is v²/r = 0.0141 m/s².

Total acceleration will be 0.0141 +0.0337 =0.0478m/s².

Thus, if you’re heading due North, total acceleration will be 0.0478 m/s².

b) If the boat goes along East, Coriolis acceleration is in the direction of centrifugal force.

Coriolis acceleration is (2 x 7.27 x 10⁻⁵ x300 ) = 0.0436m/s².

Total centrifugal acceleration due to centrifugal force = 300 +  (7.27 x 10⁻⁵ x 6371 x 10³) = 0.0436 m/s².

Total acceleration is 0.0436 + 0.0367 = 0.0803m/s².

Thus, if you’re heading due East, acceleration will be 0.0803 m/s².

c) When boat is going upward, centrifugal force will change with time. but Coriolis acceleration remains same.

Thus, if you’re heading straight up, no exact value for acceleration.

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discribe how standard of meter,second, and kilogram are agreed internationally.​

Answers

Answer:

Hindi ko Po alm sorry Po talaga

Rajani had bought a new bottle of pickle from the market. She tried to open the
metal cap but could not do so. She then took a bowl of hot water and immersed
the upper end of the bottle in it for five minutes. She could easily open the
bottle now. Why?
BEST ANSWER WILL BE MARKED

Answers

Answer:

The pickle bottle cap on dipping it in hot water expanded.

Explanation: Hope it helps you:))))

Have a good day

Which is the smallest unit of life?

Answers

Answer:

the cell is the smallest unit

The iron rim is made slightly smaller than the wooden wheel. How is this rim fitted on the wooden wheel?


BEST ANSWER WILL BE MARKED AS BRAINLIEST

Answers

Answer:

The rim is usually heated before fixing into the wooden wheel because on heating the iron rim, it expands first, then on cooling contracts and fits onto the wooden wheel.

Explanation: Hope it helps you :))))

Have a good day

When you throw a ball into the air, its kinetic energy _

Answers

Answer:

increases

Explanation:

The ball's kinetic energy is the energy it has due to its motion. When you throw the ball into the air, it gains kinetic energy from the force of your throw.

in previous years. you were taught about the three basic food groups. in this activity, classify the focos into GO, GROW or GLOW

Answers

There are three basic food groups. The foods are classified into Go, Grow and Glow.

What is a GO food?

Go Foods are the type of food that provide fuel and help us 'go' and be active whole day. 'Go' foods are: bread, rice, pasta, cereals and potato.

Grow foods are the ones which makes us grow by giving muscle strength and purifies blood.

Glow foods are the one which make us glow by face and skin healthy.

Foods classified into the three groups:

Toast+ Eggs  + Spinach : GO -GROW-GLOW

oatmeal + nuts + berries : GO -GROW-GLOW

stir fried tofu + broccoli + rice : GROW-GLOW -GO

toast + apples + peanut butter: GO -GROW-GLOW

crackers+ hummus + cucumber  :GO -GROW-GLOW

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What is the importance of science to your life? ​

Answers

Answer:

The beauty of science is everywhere.

Explanation:

science is extremely important and you see it all around you. For instance you need knowledge of chemistry to create medication in order to help cure the sick. Knowledge of physics is needed in order to construct building or vehicles.

make sure to ask if you need anymore examples or proof :)

An electric current is characterized by which of the following?
a. Charges that are stationary
b. Charges that move
c. Potential energy in a battery
d. Mechanical energy in a system
Help pls

Answers

Answer:

B. Charges that move.

How does the period of a wave change if the frequency increases by a factor of three?

Answers

Answer:

Period becomes 1/3 of the original

Explanation:

Period = 1/f      if f becomes 3f   then period becomes 1/3 of the original

A kangaroo is capable of jumping to a height of 2. 62 m.

Answers

that’s crazy ngl i cant even jump 10 feet fr

How many fluorine atoms are in a molecule of the compound arsenic
pentafluoride?
O A. 6
O B. 1
C. 2
O D. 5

Answers

Answer:

d: 5

Explanation:

arsenic pentafluride contains 6 total atoms (5 fluorine atoms)

The power in a circuit is 2 W and the voltage is 20 VDC. What's the circuit current?

Answers

Answer:

Power in the circuit is 0.1 amp

Explanation:

The power in the circuit is given by the formula

      P = V x I

Where P is Power, V is voltage supplied and I is current in circuit.

so,      I = P/v

            = 2/20

            =0.1 A

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Spring constant here for 22 cm spring is 50 N per metre 840 if you stretch the spring and when is measured again is 32 cm long what is the size of this force

Answers

K= fx => f = k/x => 50N/100cm / 10 cm = 5/10= 0.5 N

Near the surface of the Earth there is an electric field of about 150 V/m which points downward. Two identical balls with mass 0.321 kg are dropped from a height of 2.15 m , but one of the balls is positively charged with q1 = 360 μC , and the second is negatively charged with q2=-360 μC .

Use conservation of energy to determine the difference in the speeds of the two balls when they hit the ground. (Neglect air resistance.)
v+−v− =

Answers

The difference in the speeds of the two balls when they hit the ground is mathematically given as

V=0.10m/s

What is the difference in the speeds of the two balls when they hit the ground.?

Generally, the equation for Acceleration due to  electric field is mathematically given as

[tex]A=g+\frac{q1E}{m}\\\\Therefore\\\\A=9.8*\frac{600*1000*150*}{0.520}\\\\A=9.97m/s2[/tex]

For Negative charge

[tex]A=g+\frac{q1E}{m}\\\\A=9.8*\frac{-600*1000*150*}{0.520}\\\\A=9.62m/s2[/tex]

In conclusion, the speed of the negative ball

[tex]v1=\sqrt{2ah}\\\\v1=\sqrt{2*9.67*2m}[/tex]

v1=6.21m/s

The  difference in v

V=v1-v2

V=6.31-6.21

V=0.10m/s

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In 1986, a 35 × 10' kg watch was demonstrated in Canada. Suppose this
watch is placed on a huge trailer that rests on a lightweight platform, and
that oscillations equal to 0.71 Hz are induced. Find the trailer's mass if the
platform acts like a spring scale with a spring constant equal to 1.0 x 10° N/m

Answers

The mass of the trailer would be 0.10 kg

What is the period of a mass spring system?

The period of a mass spring system is said to be directly proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

It is represented thus;

T = 2π × √ m ÷ k

But note that period (T) is the reciprocal of frequency (f)

So, T = 1 ÷ f

Then, T = 2π × √ m ÷ k = 1 ÷ f

Make the mass 'm' the subject of the formula

m = k ÷ 2π^2 × f^2

Where

m = mass

k = spring constant

f = frequency

π = 3. 14

Mass, m = 1. 0 × 10^ 0 ÷ 2× 3.14 × 3.14 × 0.71 × 0. 71

= 1.0 × 1 ÷ 9. 94

= 0. 10 kg

Therefore, the mass of the trailer would be 0. 10kg.

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What is the unit of electrical power?

Answers

Answer:

Watts

Explanation:

A Watt is the unit of electrical power equal to one ampere under the pressure of one volt.

Using a refracting telescope, you observe the planet Mars when it is 1.99×1011 m from Earth. The diameter of the telescope's objective lens is 0.977 m . What is the minimum feature size, in kilometers, on the surface of Mars that your telescope can resolve for you? Use 563 nm for the wavelength of light.

Answers

The minimum feature size, in kilometers, on the surface of Mars that your telescope can resolve for you is  140km.

What is telescope?

Telescope is device through which we can see the distant objects very clearly as it seems like they are some meters away.

Distance of the Mars from the Earth D = 1.99 x 10¹¹ m

Diameter of telescope's objective lens d = 0.977 m

The wavelength of light λ in m, λ = 563nm = 563 x 10⁻⁹ m

The distance y or the minimum feature size  =1.22λD/d

Substitute the value, we get

y = 1.22 x 563 x 10⁻⁹ x 1.99 x 10¹¹ /0.977

y = 140 km (approximately)

Thus, the minimum feature size, in kilometers, on the surface of Mars that your telescope can resolve for you is  140km.

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The space station is 4.41 x 10^5 kg and orbits the earth 6.78 x 10^6 m from the center of earth. The mass of earth is 5.97 x 10^24 kg. What is the gravitational force between these two objects?

Answers

Answer:

3 820 885 N

Explanation:

Gravitational equation

   F = G  m1 m2 / r^2    

         G = gravitational constant = 6.6713 x 10^-11 m^3/kg-s^2

F = 6.6713 x 10^-11   *   4.41 x 10^5  * 5.97 x 10^24  / ( 6.78x 10^6)^2

 = 3820885 .3 N

How did pinkish white skin evolve from dark skinned populations?

1-2 sentences

Answers

Answer:Migration

Explanation: People began to migrate to areas with less UV and cooler regions. Due to the fact there was less heat, their skin tones began to get lighter. An example is in Europe where the people are generally lighter and those countries have cooler climates compared to Africa where the climate is warmer and has darker skinned people. Hope this helped!

Erwin Schrödinger developed the quantum model of the atom. What scientific knowledge was necessary for Schrödinger’s work?

Answers

The scientific knowledge was necessary for Schrödinger’s work is the discoverd of electron.

What is electron and how was it discovered?

Thomson carried out new experiments that led him to conclude that cathode rays were formed by particles that have a negative charge. Later, Thomson proved that these rays were deflected by applying an electric field. Thus, these particles were called electrons.

The discovery of the electron allowed Schrodinger to explain quantum models that are based on how electrons behave.

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with detailed explaniation

Answers

Ø=37°Initial velocity=u=20m/sg=10m/s²

#A

[tex]\\ \rm\Rrightarrow H_{max}=\dfrac{u^2sin^2\theta}{2g}[/tex]

[tex]\\ \rm\Rrightarrow H_{max}=\dfrac{20^2(sin37)^2}{2(10)}[/tex]

[tex]\\ \rm\Rrightarrow H_{max}=\dfrac{400sin^237}{20}[/tex]

[tex]\\ \rm\Rrightarrow H_{max}=20sin^237[/tex]

[tex]\\ \rm\Rrightarrow H_{max}=7.2m[/tex]

#B

[tex]\\ \rm\Rrightarrow R=\dfrac{u^2sin2\theta}{g}[/tex]

[tex]\\ \rm\Rrightarrow R=\dfrac{20^2sin74}{10}[/tex]

[tex]\\ \rm\Rrightarrow R=40sin74[/tex]

[tex]\\ \rm\Rrightarrow R=38.5m[/tex]

#C

[tex]\\ \rm\Rrightarrow T=\dfrac{2usin\theta}{g}[/tex]

[tex]\\ \rm\Rrightarrow T=\dfrac{2(20)sin37}{10}[/tex]

[tex]\\ \rm\Rrightarrow T=4sin37[/tex]

[tex]\\ \rm\Rrightarrow T=2.4s[/tex]

Now

[tex]\\ \rm\Rrightarrow v=u-gt[/tex]

[tex]\\ \rm\Rrightarrow v=20-10(2.4)[/tex]

[tex]\\ \rm\Rrightarrow v=20-24[/tex]

[tex]\\ \rm\Rrightarrow v=-4m/s[/tex]

a pool ball is rolling along a table3 with a constant velocity. the components of its velocity vector are Vx=0.5 m/s and Vy=0.8 m/s. Calculate the distance it travels in 0.4 s

Answers

The distance traveled by the pool ball is 0.376 m.

To calculate the distance traveled by the ball, we need to first find the resultant velocity of the ball.

What is resultant velocity?

This is the single velocity obtained when two or more velocities are combined.

To calculate the resultant velocity, we use the formula below.

Formula:

Vr = √(Vx²+Vy²)............. Equation 1

Where:

Vr = Resultant velocity.

From the question,

Given:

Vx = 0.5 m/sVy = 0.8 m/s

Substitute these values into equation 1

Vr = √(0.5²+0.8²)Vr = √(0.25+0.64)Vr = √(0.89)Vr = 0.94 m/s

Finally, to calculate the total distance, we use the formula below.

Formula:

d = (Vr)t.......... Equation 2

Where:

d = Distance traveled by the ballt = time

From the question,

Given:

Vr = 0.94 m/st = 0.4 s

Substitute into equation 2

d = 0.4×0.94d = 0.376 m

Hence, the distance traveled by the pool ball is 0.376 m.

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An object is placed 4.0 cm to the left of a convex lens with a focal length of +8.0 cm . Where is the image of the object?

Answers

The image of the object is 8cm to the left of the lens (D)

What is the image of an object?

The image of an object is said to be the location where light rays from that object intersect with a mirror by reflection.

It is calculated thus:

1÷v = 1÷f - 1÷u

How to calculate the image of an object

From the formula

1÷v = 1÷f - 1÷u

Where

V = image distance fromthe object

U = object

f = focal length

Substitute the values

1÷v = 1÷8 - 1÷ 4

1÷v = - 1÷8

Make v the subject of formula

v = -8cm

Therefore, the image of the object is 8cm to the left of the lens (D)

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A gas is contained in a chamber such as that in Figure 15.4. Suppose that the region outside the chamber is evacuated and the total mass of the block and the movable piston is 135 kg. When 2050 J of heat fl ows into the gas, the internal energy of the gas increases by 1730 J. What is the distance s through which the piston rises?

Answers

0.24 m  distance  through which the piston rises.

we have given the mass of piston+block = 135kg

2050 joule of heat flows into the gas

now;

According to first law thermodynamics,

dQ=du+dw

we have

2050=1730+MgS

Here M is mass, g is gravity, S is distance

now puttin gthe formula

MgS=320

S=320/1323

S= 0.24m

The link between the heat and work produced and the system's internal energy is explained by the first law of thermodynamics. The whole amount of energy present in a system, including the kinetic energy of molecules and the energy held inside their chemical bonds, is referred to as internal energy. The first law of thermodynamics states that the heat transferred into the system less the work done by the system equals the change in internal energy of the system. The law explains how energy is conserved when thermodynamic processes take place between two or more equilibrium states.

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wood is a better insulator than glass so why is fiberglass commonly used as an insulator in wooden buildings why?

Answers

Answer:

So that it may trap the solar radiations and maintain the temperature of the wooden building.

Explanation:

Wood is not as effective an insulator as fiberglass. It comes in a number of widths, the widest being 3/4 inch, which has an R-value of 0.94. However, fiberglass, the thinnest of which is 3/4 inch, has an R-value of 3. Therefore, fiberglass is a better insulator.

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