Consider a point charge qqq in three-dimensional space. Symmetry requires the electric field to point directly away from the charge in all directions. To find E(r)E(r)E(r), the magnitude of the field at distance rrr from the charge, the logical Gaussian surface is a sphere centered at the charge. The electric field is normal to this surface, so the dot product of the electric field and an infinitesimal surface element involves cos(0)=1cos⁡(0)=1. The flux integral is therefore reduced to ∫E(r)dA=E(r)A(r)∫E(r)dA=E(r)A(r), where E(r)E(r)E(r) is the magnitude of the electric field on the Gaussian surface, and A(r)A(r)A(r) is the area of the surface.

Answers

Answer 1

Answer:

 E = [tex]\frac{1}{4\pi \epsilon_o } \ r^2[/tex]

Explanation:

For this exercise let's use Gauss's law. The Gaussian surface that follows the symmetry of the charges is a sphere

           Ф = ∫ E. dA = [tex]\frac{x_{int} }{\epsilon_o}[/tex]

the bold are vectors, the radii of the sphere and the electric field are parallel therefore the scalar product reduces to the algebraic product

           Ф = ∫ E dA = \frac{x_{int} }{\epsilon_o}

           E ∫ dA = \frac{x_{int} }{\epsilon_o}

           E A = \frac{x_{int} }{\epsilon_o}

the area of ​​a sphere is

            A = 4π r²

the charge inside the sphere is q = + q

           

we substitute

           E 4π r² = \frac{x }{\epsilon_o}

           E = [tex]\frac{1}{4\pi \epsilon_o } \ r^2[/tex]


Related Questions

What is the resultant force on the human cannonball in the
vertical direction when she is flying through the air?

Answers

Answer:

heart

Explanation:

The body weighing 3.5 kg moves in the horizontal plane under the action of force F. During 3 s of movement the body traverses the path 25 m. Find the value of the force F acting on the body. Friction to be neglected.

Answers

Answer:

given..

m= 3.5

t= 3

d=25

f=?

now....a...

25=1/2a×9

a=50/9

f=ma=35/10×50/9=19.4N

Need help ASAP
Will mark BRAINLIST and thanks only for correct answers

1.Which property of AM frequencies allow them to travel over long distances?

-high amplitude
-high energy
-constant velocity
-long wavelength

2.what types of waves do cell phones use?
-radio waves
-gamma rays
-microwaves

Answers

The answer for 2 is most definitely radio waves

What is the best example of a compound machine

Answers

Answer:

chemical resemblance is physically indolence

Explanation:

Due to H2O hypermolecules

Answer:

The two basic families of simple machines are the lever family and the inclined plane family. Within the lever family are the simple lever, the pulley and the wheel and axle. Within the inclined plane family are the simple inclined plane, the wedge and the screw. These simple machines create mechanical advantage when you use them, as they allow you to exert more force with less energy on loads that you could not ordinarily move.

Explanation:

A bus travelling 30.0 km/h east has a constant increase in speed of 1.5 m/s. What is its velocity 6.8s later

Answers

The final velocity of the bus  is 9.83 m/s

The given parameters;

initial velocity of the bus, = 30 km/h

constant increase in speed, = 1.5 m/s

time of motion, t = 6.8 s

The initial velocity of the bus in m/s;

[tex]v = 30 \frac{km}{h} \times \frac{1000 \ m}{1 \ km} \times \frac{1 \ h}{3600 \ s} = 8.33 \ m/s[/tex]

The acceleration of the bus;

[tex]a = \frac{\Delta v}{\Delta t} = \frac{1.5 \ m/s}{6.8 \ s } = 0.22 \ m/s^2[/tex]

The final velocity of the bus at the given time of motion;

[tex]v= u + at\\\\v = 8.33 + (0.22 \times 6.8)\\\\v = 9.83 \ m/s[/tex]

Thus, the final velocity of the bus  is 9.83 m/s

Learn more here: https://brainly.com/question/17956487

Which of these are physical properties of matter
a. flammability
b. reactivity
c. color
d. hardness
a and b
c and d

Answers

Answer:

I believe c and d is the answer because a and b are more material properties.

D because it doesn’t need chemicals in order for it to change

Georgia drops a brick from the top of an 80.0 m building. What is the velocity of the brick when it hits the ground?

Answers

Answer:

the velocity of the brick when it hits the ground is 39.60 m/s

Explanation:

Given;

height through which the ball is dropped, h = 80.0 m

the initial velocity of the brick, u = 0

The final velocity of the brick when it hits the ground is calculated as;

v² = u² + 2gh

v² = 0 + 2 x 9.8 x 80

v² = 1568

v = √1568

v = 39.60 m/s

Therefore, the velocity of the brick when it hits the ground is 39.60 m/s

What is the change in internal energy if a gas loses 80 joules of heat, and then does 60
joules of work?

Answers

Answer:

-140

Explanation:

A gas loses 80joules of heat.

The gas also does 60 joules of work

Therefore the change in internal energy can be calculated as follows

= -80 + (-60)

= -80-60

= -140

Hence the change in internal energy is -140

If opposing forces acting on an object are equal, the net force is
N. (Enter your answer in the numerical form)

help me please

Answers

Answer:

0 N

Explanation:

suppose, you push a box with 5 N, and another person pushes the box on the opposite side of the box with 5 N, the net force (resultant ) is 0 N, the box will not move if it wasn't moving

hope this helps

What is a molecule?

Answers

Answer:

A molecule is defined as two or more atom of same element or different element grouped together

Simple definition: A molecule is a group of two or more atoms chemically bonded together.

I hope this helped a little bit :)

Please Help!!!!!!!!!!!! (physics)​

Answers

2a) moment = 1.5P
2bi) 210*1 = 210Nm
2bii) 140N
2biii) 70 N

What type of reaction is below?

Answers

Answer:

B) Synthesis

Explanation:

A combination reaction, also known as a synthesis reaction in chemistry, is when two or more substances, or reactants, combine with each other to form a new product. The product will always be a compound.

Synthesis

Hope this helps!

PLS ANSWER FAST WILL GIVE BRAINLY TIMED TEST


use the equation solving a= F divided by M


Also use metres per second squared [m/s2]



A loaded coal wagon with a total mass of 20, 000 kg is pushed by a force of 300,000 N. What was the wagon's acceleration?

Answers

a=F/m
a=(3000000)/(20000)
a=15 m/s^2

Water vapor is an example of a(n)

Answers

Answer:

Water vapor is steam. An example of water vapor is the floating mist above a pot of boiling water. Water in the form of a gas; steam.

Explanation:

how do different types of motion affect forces?

Answers

Answer:

A force is a push or pull on an object. Forces usually cannot be seen but their effects can.

Nothing moves, changes speed, stops or changes direction without force. Heavier objects need more

force to get them to move or change direction.

Explanation:

This empty trunk has a mass of 10 kilograms. The weights also have a mass of 10 kilograms. If the weights are placed in the trunk, what will be its mass? How will this affect the force needed to accelerate the trunk?

Answers

Answer:

20 kg

More force required after placing weight in trunk to accelerate the trunk than before when the trunk is empty.

Explanation:

We are given that

Mass of empty trunk, m=10 kg

Mass of a weight, m'=10 kg

We have to find the total mass after placing weight in trunk and how will this affect the force needed to accelerate the trunk.

Total mass =m+m'

Total mass=10+10=20 kg

We know that

Force, F=ma

Force is directly proportional to mass.

When we placed weight in trunk then the mass of trunk increases .Therefore, now more force required to accelerate the trunk than before when the trunk is empty.

a red shirt appears red because?

a. the shirt reflects red light

b. the shirt absorbs red light

c. the shirt emits green and blue light

d. the shirt reflects magenta and blue light

Answers

Red shirt appears red because:

a. The shirt reflects red light

A red shirt appears red because the shirt reflects red light.

Thus, An important topic for astronomers is "red shift." The phrase can be taken literally; when the light's wavelength is extended, the light is perceived as having "shifted" toward the red portion of the spectrum.

When a source of sound moves in relation to an observer, sound waves experience a similar phenomenon.

The frequency of sound waves varies if the source of the sound and the observer are moving relative to one another, according to Austrian mathematician Christian Andreas Doppler, who made this discovery.

The observer hears a frequency that is higher when the two are moving closer together and lower when they are moving farther apart and red shift.

Thus, A red shirt appears red because the shirt reflects red light.

Learn more about Red shift, refer to the link:

https://brainly.com/question/30847331

#SPJ6

4. A weightlifter raises a mass mat a constant speed to a height h in time t. Which of the following
expressions corresponds with the work done by the weightlifter?
a. mgh
b.-mgh
C. mgh/t
d. -mgh/

Answers

Answer:

a. mgh

Explanation

The work done by the lifter is equal to its potential energy since he is covering a height and under the influence of gravity.

potential energy = mass * acceleration due to gravity * height

m is the mass

g is the acceleration due to gravity

h is the height

Hence the required workdone = PE = mgh

You first walk 8.0 km north from home, then walk east until your displacement from home is 10.0 km. How far east did you walk?

Answers

You use Pythagorean theorem

10^2 = 8^2 + b^2
100 = 64 + b^2
b^2 = 36
b = 6

You walked 6km east

A cannonball has just been shot out of a cannon aimed 45∘ above the horizontal rightward direction. Drag forces cannot be neglected.

Answers

Answer:

The free-body diagram of the cannonball is found in the attachment below

Note The question is incomplete. The complete question is as follows:

A cannonball has just been shot out of a cannon aimed 45∘ above the horizontal rightward direction. Drag forces cannot be neglected.

Draw the free-body diagram of the cannonball.

Explanation:

Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.

In order to construct free-body diagrams, it is important to know the various types of forces acting on the object in that situation. Then, the direction in which each of the forces is acting is determined. Finally the given object is drawn using any given representation, usually a box, and the direction of action of the forces are represented using arrows.

In the given situation of a cannonball which has just been shot out of a cannon aimed 45∘ above the horizontal rightward direction., the forces acting on it are:

F = force exerted by the cannon acting in the direction of angle of projection

Fdrag = drag force. The drag force acts in a direction opposite to the force exerted by the cannon

Fw = weight of the cannonball acting in a downward direction

The free body diagram is as shown in the attachment below.

What is the amount of nickel, which has an average atomic mass of 58.7 amu, present in 525 g nickel

Answers

Answer:

bhgyg 78 gt78gyug

Explanation:

Answer:77.98

Explanation:

HELP IT'S DUE TOMORROW ;w;
Give an example of each of the following types of matter:

a) heterogeneous mixture:
b) homogeneous mixture:
c) element:
d) compound:

Answers

Answer:

A) A tossed salad
B) Milkshake
C) helium
D) NaCl (sodium and chlorine)


Explanation: hope this helps

if you wanna make it easier you can number them going down 1,2,3, or 4 & just tell me the number

Answers

the number is 1 I hope this help

Three point charges are arranged along the x axis. Charge q1 = -4.10 nC is located at x= 0.250 mand charge q2 = 2.20 nC is at x= -0.320 m . A positive point charge q3 is located at the origin.


What must the value of q3 be for the net force on this point charge to have magnitude 3.10 μN ? (ans in nC)


What is the direction of the net force on q3? + or - direction


Where along the x axis can q3 be placed and the net force on it be zero, other than the trivial answers of x=+[infinity] and x=−[infinity]? (ans in m)

Answers

Answer:

1) q₃ is approximately -7.58 nC

2) The direction of the net force on 'q₃' is the negative '-' direction

3) For the net force on 'q₃' to be zero, 'q₃' can be placed at x = -0.079 m or x = -1.881 m

Explanation:

1) The force, 'F', between two charged spheres is given as follows;

[tex]F = \dfrac{k \cdot q_1 \cdot q_2}{r^2}[/tex]

The net force acting on the point charge, 'q₃', is given as follows;

[tex]F_{NET} = \dfrac{k \cdot q_1 \cdot q_3}{x_1^2} + \dfrac{k \cdot q_2 \cdot q_3}{x_2^2}[/tex]

By substituting the given values, we have;

[tex]F_{NET} = 3.10 \ \mu N = \dfrac{k \cdot (-4.10 \ nC) \cdot q_3}{(0.250 \ m) ^2} + \dfrac{k \cdot 2.20 \ nC \cdot q_3}{(-0.320 \ m)^2}[/tex]

[tex]3.01 \ \mu N= q_3 \cdot \left ( \dfrac{k \cdot (-4.10 \ nC) }{(0.250 \ m) ^2} + \dfrac{k \cdot 2.20 \ nC }{(-0.320 \ m)^2} \right) = -\dfrac{14117 \ nC \cdot K}{320}[/tex]

[tex]\therefore q_3 = 3.01 \ \mu N \times -\dfrac{320 \ m^2}{14117 \ nC \cdot K}[/tex]

K = 9 × 10⁹ N·m²·C⁻²

[tex]\therefore q_3 = 3.01 \ \times 10^{-6} \ N \times -\dfrac{320 \ m^2}{14117 \times 10^{-9} \ C \times 9 \times 10^9 \ N \cdot m^2 \cdot C^{-2}}= -7.58 \ nC[/tex]

q₃ ≈ -7.58 nC

2) Given that the negative charge, 'q₁' (-4.10 nC), is located at x = 0.250 m, which is on the positive, '+' side of the origin, it will repel the negatively charged 'q₃', to the '-' direction. q₃ will also be attracted to the '-' direction by the positively charged 'q₂' which is at -0.320 m on the negative side of the origin

The net force's direction on q₃ will be in the '-' direction

3) For zero net force, we have;

The distance between the given point charges, r = 0.250 - (-0.320)) = 0.57 m

Let 'r1' represent the distance between 'q1' and 'q3', therefore, the distance between 'q2' and 'q3' is 0.57 - r1

By substitution, we have;

[tex]0 \ N= q_3 \cdot \left ( \dfrac{k \cdot (-4.10 \ nC) }{(0.57 - r_1 ) ^2} + \dfrac{k \cdot 2.20 \ nC }{(r_1)^2} \right)[/tex]

[tex]\therefore \dfrac{k \cdot 4.10 \ nC }{(0.57 - r_1 ) ^2} = \dfrac{k \cdot 2.20 \ nC }{(r_1)^2}[/tex]

From which we have;

[tex]\dfrac{4.10 \ nC }{(0.57 - r_1 ) ^2} = \dfrac{2.20 \ nC }{(r_1)^2}[/tex]

(r₁)²×4.10 = 2.20 × (0.57 - r₁)²

From the above equation, we have;

95,000·r₁²+ 125,400·r₁-35739 = 0

Solving, using a graphing calculator we get;

r₁ ≈ 0.241 or r₁ ≈ -1.561

Where, 'r₁', is measured from 'q₂', therefore, we have;

r₁ = 0.241 + (-0.320) ≈ -0.079 or r₁ = -1.561 + (-0.320) ≈ -1.881

Therefore, the charge 'q₃' can be placed at x = -0.079 or x = -1.881 for the ne force on it to be zero

A car takes 10 s to go from vi=0 m/s to vf=25 m/s. How far does the car travel in
that time?

Answers

Answer:

2.5 k

Explanation:

Which force is exerted by all matter on all other matter?

Answers

Answer:

Gravity

Explanation:

Gravity, also called gravitation, in mechanics, the universal force of attraction acting between all

The answer is gravity

How is the wave speed calculated?

Answers

Wave Speed = wavelength x frequency

7. The sketch shows a painter standing on a

scaffold that is supported by two ropes. The

person weighs 500 N and the force of each

rope is 400 N. Calculate the weight of the

scaffold.

Fr

Answers

Answer:

300N

Explanation:

From the question

Weight of painter = 500N

Weight of scaffold = x

Weight of painter + weight of scaffold = 2* 400 (since they are supported by two ropes)

Substitute

500 + x = 2(400)

500+x = 800

x =  800-500

x = 300N

Hence the weight of the  scaffold is 300N

11. What is the difference between AM radio waves and FM radio waves?

Answers

Answer:

they amplitude modulation

and they ferequency modulation

Explanation:

The difference is in how the carrier wave is modulated, or altered. With AM radio, the amplitude, or overall strength, of the signal is varied to incorporate the sound information. With FM, the frequency (the number of times each second that the current changes direction) of the carrier signal is varied.

hope it helps

a b c or d about the earth...
this is easy if u know

Answers

Answer:

A

Explanation:

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