State and explain Gauss's law in
electrostatics and use it to determine the electric field
intensity due to a line charge.

Answers

Answer 1

To find:-

To find the electric field due to a point charge using Gauss's Law .

Answer:-

Gauss's law in electrostatics states that the electric flux through a closed surface is equal to 1/ε0 times the charge enclosed by that surface, that is,

\(\implies \displaystyle \phi_E = \oint \vec{E} .\vec{ds} \\\)

Also ,

\(\implies\displaystyle \oint \vec{E}.\vec{ds} =\dfrac{q}{\epsilon_0} \\\)

Linear density of charge:-

It ise defined as charge per unit length. Mathematically,

\(\implies\displaystyle \lambda =\dfrac{q}{\ell} \\\)

where ,

\( q\) is the charge .\(\ell\) is the length of the conductor.

For figure see attachment.

Now let us assume that the linear density of charge is \(\lambda\) . There is a point P near the wire at a distance of " r " from it , where we are interested in calculating the electrical field. Imagine a coaxial Gaussian cylinder of length \(\ell\) , and radius " r " such that the point P lines on its surface.

Calculating Electrical flux through the cylinder:-

\(\implies\displaystyle \phi_E = 0 + 0 + \oint E.ds \\\)

\(\implies\displaystyle\phi_E = \oint E.ds \ \cos0^o \\\)

\(\implies\displaystyle \phi_E = \oint Eds \\\)

\(\implies\displaystyle \phi_E = E\oint ds \\\)

\(\implies\displaystyle \phi_E = E (2\pi r\ell) \ \ dots (1) \\\)

From Gauss's law:-

\(\implies\displaystyle \phi_E =\dfrac{q}{\epsilon_0} \\\)

\(\implies\displaystyle \phi_E = \dfrac{\lambda \ell}{\epsilon_0}\ \dots (2) \\\)

Therefore , from equation (1) and (2) , we have;

\(\implies\displaystyle E \times 2\pi r \ell =\dfrac{\lambda\ell}{\epsilon_0}\\\)

\(\implies\displaystyle \underline{\underline{\green{ E =\dfrac{1}{4\pi \epsilon_0}\dfrac{2\lambda}{r}}}}\\\)

And we are done!

State And Explain Gauss's Law Inelectrostatics And Use It To Determine The Electric Fieldintensity Due

Related Questions

Usually you walk straight home from school. But today you take
a detour to buy some candy on the way home. Which will
change, the distance of our walk home, the displacement of
your walk home, or both?

Answers

Answer: the distance of our walk home.

Explanation:

In Physics when we speak of distance we refer to the space traveled that is always measured on the trajectory, while displacement refers to the space from an initial position to a final position regardless of the path. When the path is a straight line, the space traveled is equal to the module of the displacement.

Spymore

3. A car waits at a red light for a few seconds, and then accelerates straight ahead to 54 km/h
in 3.1 s and then cruises at a constant speed for 75 m. The road is straight. Find the total
distance and time travelled

Answers

In the first 3.1 s, the car accelerates with acceleration a from rest to a speed of 54 km/h = 15 m/s, so its acceleration is

15 m/s = a (3.1 s)

a = (15 m/s) / (3.1 s)

a ≈ 4.8 m/s²

So in this time, it travels a distance of

x = 1/2 (4.8 m/s²) (3.1 s)²

x = 23.25 m

For the remaining time, it moves at a constant 15 m/s, covering a distance x of

x = (15 m/s) t

for until it moves 75 m, which takes

75 m = (15 m/s) t

t = (75 m) / (15 m/s)

t = 5 s

So, the car travels a total distance of 98.25 m in 8.1 s.

when wind encounters a wind turbine that produces energy, wind speed on the downside of the blades is

Answers

It is slowed
Can I get Brainliest

A string is waved up and down to create a wave pattern with a wavelength of 0.5 m. If the waves are generated with a frequency of 2 Hz, what is the speed of the wave that travels through the string to the other end?

Answers

Wave speed = (wavelength) x (frequency)

Wave speed = (0.5 m) x (2 /sec)

Wave speed = 1 m/s

The speed of light is 3×10^8 meters per second, which means that light can travel 300 million meters in just one second. How far can light travel in one minute?

Answers

Answer:

(1.8 × 10^9) meters in one minute

Explanation:

To determine how far light can travel in one minute, we need to multiply its speed by the number of seconds in a minute.

The speed of light is 3 × 10^8 meters per second.

There are 60 seconds in a minute.

Therefore, the distance light can travel in one minute is:

Distance = Speed × Time

Distance = (3 × 10^8 meters per second) × (60 seconds)

Calculating this, we get:

Distance = 3 × 10^8 meters/second × 60 seconds

Distance = 18 × 10^8 meters

Distance = 1.8 × 10^9 meters

So, light can travel approximately 1.8 billion (1.8 × 10^9) meters in one minute.

Explain how and why energy is important to living things. Your answer to this question will become the claim for your scientific explanation. There are many different ways that scientists communicate scientific explanations—through models, diagrams, data charts, graphs, written text, and oral presentations.

if someone can help me thanks ​

Answers

Answer:

All the different materials that make up our world – the elements listed on the periodic table – are all made up of atoms. The particles that make up atoms – protons, neutrons, and electrons – are condensed forms of energy that interact with each other and give rise to an element’s characteristics.

Explanation:

what does personal mission statement?

Answers

Answer:

A personal mission statement defines who you are as a person (or as a team member where you work) and identifies your purpose, whether that's in the office or simply in life.

Explanation:

It explains how you aim to pursue that purpose, and why it matters so much to you.

NEED HELP What color is the container for R-134a refrigerant? A. Light blue B. Yellow C. Dark green D.White and yellow​

Answers

Answer:

It is A. Light blue

_____________

Hope this helps!

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╭━┻╮╲┗━━━━╮╭╮┈

┃▎▎┃╲╲╲╲╲╲┣━╯┈

╰━┳┻▅╯╲╲╲╲┃┈┈┈

┈┈╰━┳┓┏┳┓┏╯┈┈┈

┈┈┈┈┗┻┛┗┻┛┈┈┈┈

two physical quantities that change with temperature​

Answers

Answer:

i think this is wat u want

two physical quantities that change with temperature

A 5kg block starts from rest and slides down 4m along a 30° inclined plane. Find the change in kinetic energy

Answers

Answer:

Let

F

be horizontal force applied on the block as shown above.This force will have two components

(1)

F

cos

30

that will act upward parallel to inclined plane.

(2)

F

sin

30

that will act on inclined plane perpendicularly. So it will be added with the component of the weight of the block

5

g

cos

30

to enhance the magnitude of Normal reaction

N

So the frictional force

f

fric

=

μ

N

=

0.2

(

F

sin

30

+

5

g

cos

30

)

,where acceleration due to gravity

(

g

)

=

9.8

m

/

s

2

Again the component of the weight of the block of mass 5kg acting downward parallel to the inclined plane is

5

g

sin

30

(a) Considering that the equilibrium of forces when the body is on the verge of sliding up the incline we can write

F

cos

30

=

5

g

sin

30

+

0.2

(

F

sin

30

+

5

g

cos

30

)

F

=

5

g

(

sin

30

+

0.2

cos

30

)

cos

30

0.2

sin

30

43

N

(b) Considering that the equilibrium of forces when the body is on the verge of sliding down the incline, we can write

F

cos

30

=

5

g

sin

30

0.2

(

F

sin

30

+

5

g

cos

30

)

F

=

5

g

(

sin

30

0.2

cos

30

)

cos

30

+

0.2

sin

30

16.6

N

Explanation:

iii) If 5 moles of gas at 1 atm is expanded from 50 liter from 5 liter at constant temperature of 20 °C. find the work done by the gas. (2​

Answers

The work done on the system with 5 moles of gas will be 58.33 kilojoules.

What is the work done for an isothermal process?

The Pressure is inversely balanced with the volume. Let the initial pressure and initial volume be P₁ and V₁, and the last volume be V₂.

Then the work done by the gas will be given as,

WD = P₁ V₁ ln (V₂ / V₁)

If 5 moles of gas at 1 atm is a contraction from 50 liters to 5 liters at a constant temperature of 20 °C.

WD = n P₁ V₁ ln (V₂ / V₁)

WD = 5 × 1.01325 × 10⁵ × 50 × 10⁻³ × ln (5 / 50)

WD =  25,331.25 × (-2.302)

WD = - 58327.36 J

WD = - 58.33 kJ

A negative sign represents the work is done on the system.

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what is the constant snell’s law

Answers

Snell's law is defined as “The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media”.

A 1 kg pistol, initially at rest, shoots a bullet with a mass of 2.5g. After

firing, the bullet travels at a speed of 150m/s. What will be the recoil velocity after

gun has fired?​

Answers

Answer:

Use the principle of momentum

Initial momentum = final momentum

Momentum formula = Mass * Velocity

Explanation:

Starting at rest at the top of a ski slope, you travel down the hill reaching a velocity of 20 m/s after 13 seconds. Once you reach the bottom of the hill you travel at a constant velocity of 20 m/s for the next 7 seconds. Sketch a quantitative (with numbers) position vs time, velocity vs time, and acceleration vs time graph of the skier's motion. PLEASE SHOW WORK AND I WILL MARK YOU THE BRAINLIEST

Answers

Answer:

The graphs are attached

Explanation:

We are told that he started at rest at rest and travelled down the hill reaching a velocity of 20 m/s after 13 seconds.

Acceleration is gotten from;

v = u + at

a = (v - u)/t

a = (20 - 0)/13

a = 20/13 m/s² or 1.54 m/s²

Distance in this period is gotten from;

v² = u² + 2as

s = (v² - u²)/2s

s = (20² - 0²)/(2 × 20/13)

s = 400/(40/13)

s = 130 m

We are told that after reaching the bottom of the hill, he travelled at a constant velocity of 20 m/s for the next 7 seconds.

At constant velocity, acceleration is 0.

Thus,distance in this period is;

s1 = vt = 20 × 7 = 140 m

I've attached the graphs

Starting at rest at the top of a ski slope, you travel down the hill reaching a velocity of 20 m/s after
Starting at rest at the top of a ski slope, you travel down the hill reaching a velocity of 20 m/s after
Starting at rest at the top of a ski slope, you travel down the hill reaching a velocity of 20 m/s after

An RLC circuit is used in a radio to tune into the radio lagos fm Station broadcasting at 93.5Hz. The resistance is 15ohms and the inductance is 1.6 H. Calculate the capacitance used​

Answers

The characteristics of the RLC circuit allow to find the result for the capacitance at a resonance of 93.5 Hz is:

Capacitance is C = 1.8 10⁻⁶ F

A series RLC circuit reaches the maximum signal for a specific frequency, called the resonance frequency, this value depends on the impedance of the circuit.

            \(Z^2 = R^2 + ( wL - \frac{1}{wC} )^2\)  

Where Z is the impedance of the circuit, R the resistance, L the inductance, C the capacitance and w the angular velocity. The negative sign is due to the fact that the current in the capacitor and the inductor are out of phase.

In the case of resonance, the impedance term completes the circuit as a resistive system.

           \(wL - \frac{1}{wC} = 0 \\w^2 = \frac{1}{LC}\)  

           

Indicate that the inductance L = 1.6 H and the frequency f = 93.5 Hz.

Angular velocity and frequency are related.

         

         w = 2π f

           

Let's  substitute.

          \(C = \frac{1}{L ( 2 \pi f)^2 }\)  

 

Let's calculate.

         \(C = \frac{1}{1.6 \ ( 2\pi \ 93.5)^2}\)  

         C = 1.8 10⁻⁶ F

In conclusion with the characteristics of the RLC circuits we can find the result for the capacitance at a 93.5 Hz resonance is:

Capacitance is C = 1.8 10⁻⁶ F

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Which description tells two processes scientists think move Earth's lithospheric plates?

Responses

friction between the plate and the asthenosphere and pressure of magma on the edge of the plate

friction between the plate and the asthenosphere and pressure of magma on the edge of the plate

gravity acting on the edges of plates and convection in the mantle

gravity acting on the edges of plates and convection in the mantle

gravity acting on the edges of plates and friction between the plate and the asthenosphere

gravity acting on the edges of plates and friction between the plate and the asthenosphere

convection in the mantle and pressure of magma on the edge of the plate

Answers

The description that tells two processes that scientists think move Earth's lithospheric plates is convection in the mantle and pressure of magma on the edge of the plate.

What is the Earth's lithosphere?

The Earth's lithosphere is the rocky outer part of Earth which is made up of the brittle crust and the top part of the upper mantle.

The Earth's lithosphere deflects the convections and as the convections churn clockwise of anticlockwise, they drag the  lithosphere with it via friction an this is what is stipulated to cause tectonic plate movements.  

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Answer: convection in the mantle and pressure of magma on the edge of the plate

Explanation: I took the unit test

As a boss, knowing your employees’ personality types can help you

Answers

Answer:

identify who they are as a person

Explanation:

A marine weather station reports waves along the shore that are 2 meters high, 8 meters long, and reach the station 8 seconds apart. Determine the speed of these waves.

Answers

One full weather station reports  wave passing a spot every second is equivalent to a frequency of 1 Hz. The frequency is 48=12=0.5 Hz if 4 waves pass a spot in 8 seconds.

What is the frequency of a 30-second ocean wave that hits the shore?

The number of cycles that make up a time unit is the frequency. The frequency of a wave with a 30-second period is therefore 1 30 = 0.033 cycles per second, or 0.033 Hertz (Hz).

Which of the following statements most accurately sums up how a wave crosses a border and enters a new medium?

A wave's speed and wavelength vary as it crosses a border and enters a new medium, but its frequency doesn't.

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what is a shargaff rule

Answers

According to Chargaff's rule, the amounts of adenine (A), thymine (T), and guanine (G) in the DNA molecule are equal to each other. The amounts of cytosine (C) and guanine (G) are also equal.

Who is Chargaff ?

Erwin Chargaff was a biochemist, author, Bucovinian Jew who immigrated to America during the Nazi era, and professor of biochemistry at Columbia University's medical school.

Chargaff found patterns among the four bases, or chemical building blocks, of DNA, which are directly related to DNA's function as the genetic material of living things.

He was born in Austria-Hungary. Heraclitean Fire: Sketches from a Life Before Nature, an autobiography he penned, received positive reviews.

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Revolution + tilt = what

Answers

Revolution is the movement of the Earth around the Sun. The Earth takes 24 hours to complete a rotation with respect to the sun. The Earth's axis of rotation is tilted by 23.5 degrees. This tilt causes the different seasons of the year.

You are a member of a geological team in Central Africa. Your team comes upon a wide river that is flowing east. You must determine the width of the river and the speed of the current (the speed of the water relative to the earth). You have a small boat with an outboard motor. By measuring the time it takes to cross a pond where the water isn’t flowing, you have calibrated the throttle settings to the speed of the boat in still water. You set the throttle so that the speed of the boat relative to the river is a constant vv1. Traveling due north across the river, you reach the opposite bank in tt1. For the return trip, you change the throttle setting so that the speed of the boat relative to the water is vv2. You travel due south from one bank to the other and cross the river in tt2. (a) How wide is the river, and what is the speed of the current? (b) With the throttle set so that the speed of the boat relative to the water is 6.00 m/s, what is the shortest time in which you could cro

Answers

I have no idea what this is

a 1 kg blob of putty moving at 10 m/s runs into another 1 kg stationary blob, and they stick together. the momentum of the blobs after the collision is

Answers

The momentum of the blobs after the collision of a 1 kg blob of putty moving at 10 m/s with another 1 kg stationary blob will be 5 m/s.

The term "completely inelastic collision" is used to describe every time two masses cling together after colliding. Any inelastic collision will result in the internal energy of the objects being transformed into kinetic energy. Because of this, even though the system's energy is conserved (no outside forces are at action), its internal energy is changing in an unknowable and unpredictable fashion. This implies that the concept of energy conservation in inelastic collisions is absolutely meaningless to us. However, the conserved quantity that we can monitor is momentum.

Initial momentum is expressed as p = m1v1 + m2v2,

where, I denotes vector quantities.

v2 = 0  (because the second blob is at rest).

As a result, p=m1v1, |p|=m1|v1|=1*10= 10 kg*m/s,

The total amount of momentum is conserved in a closed system. The end momentum is 10 kg*m/s and is therefore also directed in the same direction as the beginning momentum.

The combined mass is now M=m1+m2= 1+1 = 2 kg due to the fact that two blobs are now clumped together. As a result, p = mv= 10 =2v; from this, v= 10/2 = 5 m/s, headed in the same direction as the first blob's starting velocity.

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How much force is needed to stretch a spring 1.2m if the spring constant is 8.5 N/m?

Answers

Explanation:

spring constant k::8.5

and displacement x::1.2

f:? f: k×x

8.5×1.2:10.2N

Why did Galileo use a thought experiment instead of working with real objects

Answers

Answer:

Galileo thought that a ball, rolling or sliding down a hill without friction, would run up to the same height on an opposite hill.

Suppose that the opposite hill was horizontal. Would the ball's motion continue forever along the tangent, or forever parallel to the Earth's surface

Galileo's conclusion from this thought experiment was that no force is needed to keep an object moving with constant velocity.

Newton took this as his first law of motion.

Explanation:

Here ya go-

Using the Left Hand Rule, if motion is away from you and the current is left, which way is the field?
A. Down
B. Left
C. Up
D. Right

Answers

C. Up

Explanation:

To apply the Left Hand Rule, point your left thumb in the direction of the current and your left fingers in the direction of the motion. The direction in which your left palm faces is the direction of the magnetic field. In this case, if the motion is away from you (i.e., in the direction of your eyes), and the current is left, then the magnetic field will be directed upwards.

Shawn and his bike have a total mass of 49.9 kg. Shawn rides his bike 0.92 km in 15.4 min at a constant velocity. The acceleration of gravity is 9.8 m/s 2 . What is Shawn’s kinetic energy? Answer in units of J.

Answers

Answer:

0 J

Explanation:

KE = .5(m)(v2-v1)

if velocity is constant v2 = v1, then v2 - v1 = 0

therefore if (v2-v1) = 0, then KE must also be equal to 0

what is the valency of Sulphur!!​

Answers

Explanation:

The sulphur atom has 6 electrons in the outermost shell, and its valency could be 6. But it is easier for sulphur to gain two electrons instead of losing six electrons. Hence, its valency is determined by subtracting six electrons from the octet and this gives a valency of two for sulphur.

The velocity time graph of an object mass 50 g is shown in figure study graph and answer
1)calculate force acting on object in time interval 0-3 seconds
2)calculate the force acting on the object in the time interval 6-10 seconds 
3)Is there any time interval in which no force acts on object.Justify

The velocity time graph of an object mass 50 g is shown in figure study graph and answer1)calculate force

Answers

1) The force acting on the object during the time interval 0-3 seconds is 1/3 N.

2) The force acting on the object during the time interval 6-10 seconds is -0.5 N.

3) There is no time interval in which no force acts on the object.

(i) Force acting on the object in time interval 0-3 seconds. Force acting on the object is equal to the product of its mass and acceleration, i.e.,F = ma.

In the given velocity-time graph, the acceleration of the object can be determined by determining the slope of the velocity-time graph from 0 to 3 seconds.

Slope = (change in velocity) / (change in time)= (20-0) / (3-0) = 20/3 m/s^2

Acceleration, a = slope= 20/3 m/s^2

Mass of the object, m = 50 g = 0.05 kg

∴ Force acting on the object, F = ma= 0.05 × 20/3= 1/3 N.

Therefore, the force acting on the object during the time interval 0-3 seconds is 1/3 N.

(ii) Force acting on the object in time interval 6-10 seconds. Similar to the first question, the force acting on the object in time interval 6-10 seconds can be determined by determining the acceleration of the object during this time interval.

The slope of the velocity-time graph from 6 seconds to 10 seconds can be determined as follows:

Slope = (change in velocity) / (change in time)= (-20-20) / (10-6) = -40/4= -10 m/s^2 (negative sign indicates that the object is decelerating)

Mass of the object, m = 50 g = 0.05 kg

∴ Force acting on the object, F = ma= 0.05 × (-10)= -0.5 N.

Therefore, the force acting on the object during the time interval 6-10 seconds is -0.5 N.

(iii) Time interval in which no force acts on the object. There is no time interval in which no force acts on the object. This is because, as per Newton's first law of motion, an object will continue to remain in a state of rest or uniform motion along a straight line unless acted upon by an external unbalanced force.In other words, if the object is moving with a constant velocity, there must be a force acting on the object to maintain its motion.

Therefore, there is no time interval in which no force acts on the object.

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A point charge q1 has a magnitude of 3.5x10-6 C. A second charge q2 has a magnitude of -1.8x10-6 C and is located 0.15 m from the first charge. Determine the electrostatic force exerts on each other.

Answers

The electrostatic force exerts on each other is 1.134 N

Electrostatic force calculation.

The electrostatic force between the two charges is given by Coulomb's Law:

F = k * |q1| * |q2| / r^2

where k is the Coulomb constant (9.0 x 10^9 N*m^2/C^2), |q1| and |q2| are the magnitudes of the two charges, and r is the distance between them.

Substituting the given values, we have:

F = (9.0 x 10^9 N*m^2/C^2) * (3.5 x 10^-6 C) * (1.8 x 10^-6 C) / (0.15 m)^2

F = 1.134 N

The electrostatic force exerted on each charge is equal in magnitude but opposite in direction, according to Newton's Third Law. Therefore, the magnitude of the force on each charge is 1.134 N, but they point in opposite directions. The force on q1 is attractive (toward q2), while the force on q2 is repulsive (away from q1).

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If an 800 kg roller coaster is at the top of its 50 m high track, it will have a potential energy 392,000 and a kinetic energy of 0J. This means the total mechanical energy is 392,000J. If the cart drops down to a new height of 10m, how much energy does the cart have now?

Answers

ANSWER:

313600 J

STEP-BY-STEP EXPLANATION:

We have that the gravitational potential energy is given by the following equation:

\(E_p=m\cdot g\cdot h\)

We substitute and calculate the potential energy, knowing that g is the acceleration of gravity and is equal to 9.8 m/s^2:

\(\begin{gathered} E_p=800\cdot9.8\cdot10 \\ E_p=78400\text{ J} \end{gathered}\)

We know that the total energy is 392,000 joules, so the energy it now carries would be the total minus the calculated potential energy:

\(\begin{gathered} E_k=392000-78400 \\ E_k=313600\text{ J} \end{gathered}\)

The energy carried by the cart is 313600 J

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