Answers
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,
[tex]\implies \displaystyle \phi_E = \oint \vec{E} .\vec{ds} \\[/tex]
Also ,
[tex]\implies\displaystyle \oint \vec{E}.\vec{ds} =\dfrac{q}{\epsilon_0} \\[/tex]
Linear density of charge:-
It ise defined as charge per unit length. Mathematically,
[tex]\implies\displaystyle \lambda =\dfrac{q}{\ell} \\[/tex]
where ,
[tex] q[/tex] is the charge .[tex]\ell[/tex] is the length of the conductor.For figure see attachment.
Now let us assume that the linear density of charge is [tex]\lambda[/tex] . 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 [tex]\ell[/tex] , and radius " r " such that the point P lines on its surface.
Calculating Electrical flux through the cylinder:-
[tex]\implies\displaystyle \phi_E = 0 + 0 + \oint E.ds \\[/tex]
[tex]\implies\displaystyle\phi_E = \oint E.ds \ \cos0^o \\[/tex]
[tex]\implies\displaystyle \phi_E = \oint Eds \\[/tex]
[tex]\implies\displaystyle \phi_E = E\oint ds \\[/tex]
[tex]\implies\displaystyle \phi_E = E (2\pi r\ell) \ \ dots (1) \\[/tex]
From Gauss's law:-
[tex]\implies\displaystyle \phi_E =\dfrac{q}{\epsilon_0} \\[/tex]
[tex]\implies\displaystyle \phi_E = \dfrac{\lambda \ell}{\epsilon_0}\ \dots (2) \\[/tex]
Therefore , from equation (1) and (2) , we have;
[tex]\implies\displaystyle E \times 2\pi r \ell =\dfrac{\lambda\ell}{\epsilon_0}\\[/tex]
[tex]\implies\displaystyle \underline{\underline{\green{ E =\dfrac{1}{4\pi \epsilon_0}\dfrac{2\lambda}{r}}}}\\[/tex]
And we are done!
Related Questions
mechanical energy defintion
Answers
Answer: Mechanical energy is the energy that is possessed by an object due to its motion or due to its position.
(The energy acquired by the objects upon which work is done)
John and Suzie are trying to improve the speed of their race car by adjusting the angle of the rear spoiler. Which choice is the controlled variable(s)?
the maximum speed and the angle of the rear spoiler
the type of tire and the type of fuel
only the maximum speed
only the angle of the rear spoiler
Answers
Answer:
the type of tire and the type of fuel
Explanation:
a blackbody is at temperature of 500°C . What would be its temperature in Kelvin for it to radiate twice as much energy per second?
Answers
Answer:
Its temperature in Kelvin for it to radiate twice as much energy = [tex]919.257k[/tex]Explanation:
Energy = [tex]6AT^4[/tex]
therefore,
[tex]\frac{E_1}{E_2} = \frac{T_1^4}{T_2^4}[/tex]
where [tex]E_2 = 2E_1[/tex]
therefore,
[tex]\frac{E_1}{2E_1} = \frac{(500+273)^4}{T_2^4}\\\\T_2 = 919.257k\\\\T_2 = 646.257^oC[/tex]
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A crate is pulled with a force of 165 N at an angle 30°
northwest. What is the resultant horizontal force on the crate?
Help asap?
Answers
Answer: 143 N
Explanation:
Why do mirrors form inverted images?
Answers
Answer:
Explanation:
The image is real light rays actually focus at the image location). As the object moves towards the mirror the image location moves further away from the mirror and the image size grows (but the image is still inverted).
When the object is far from the mirror, the image is inverted and at the focal point. The image is real light rays actually focus at the image location). ... As the object moves towards the mirror inside the focal point the image becomes virtual and upright behind the mirror.
A freight train car has a mass of 2,000 kilograms and an acceleration of 1.8 m/s/s. What is the average force behind that train car?
Answers
Answer:
F = 3600 [N]
Explanation:
To solve this problem we must use Newton's second law, which tells us that the sum of force must be equal to the product of mass by acceleration.
ΣF = m*a
where:
F = force [N]
m = mass = 2000 [kg]
a = acceleration = 1.8 [m/s^2]
Now replacing:
F = 2000*1.8
F = 3600 [N]
In a mass spectrometer chlorine ions of mass 35u and charge 5e are emitted from a source and accelerated through a potential difference of 250 kV. They then enter a region with a magnetic field that is perpendicular to their original direction of motion. The chlorine ions exit the spectrometer after being bent along a path with radius of curvature 3.5 m. What is the speed of the chlorine ions as they enter the magnetic field region
Answers
Answer:
Explanation:
From the question we are told that
The mass of chlorine ion is [tex]m_c = 35u = 35 * 1.66*10^{-27} = 5.81*10^{-26}\ kg[/tex]
The charge is [tex]q = 5e = 5 * 1.60 *10^{-19} = 8.0*10^{-19}\ C[/tex]
The potential difference is [tex]V = 250 kV = 250*10^{3} \ V[/tex]
The radius of curvature of the path is [tex]r = 3.5 \ m[/tex]
Gnerally the magnetic force will cause the speed of the chlorine ions to change from 0 m/s to [tex]v_y[/tex] m/s along the y -axis but will not affect the velocity along the x-axis
Generally according the law of energy conservation
[tex]K = PE[/tex]
Here K is the kinetic energy of the of the chlorine ions which is mathematically represented as
[tex]K = \frac{1}{2} mv^2[/tex]
And PE is electric potential energy which is mathematically represented as
[tex]PE = Q * V[/tex]
So
[tex] \frac{1}{2} mv^2 = Q * V [/tex]
=> [tex] \frac{1}{2} * 5.81*10^{-26} * v^2 = 8.0*10^{-19} * 250*10^{3} [/tex]
=> [tex] v = sqrt{6.8847 *10^{12}} [/tex]
=> [tex] v = 2.634 *10^{6} \ m/s [/tex]
A motorcycle is stopped at a stop light. When the light turns green it
accelerates at 4.2 m/s^2. How far does it travel during 3 s? *
Answers
Answer: 18.9 m
Explanation:
i did the kinematic equation & found the answer.
(a) If two sound waves, one in a gas medium and one in a liquid medium, are equal in intensity, what is the ratio of the pressure amplitude of the wave in the liquid to that of the wave in the gas? Assume that the density of the gas is 2.27 kg/m3 and the density of the liquid is 972 kg/m3. The speed of sound is 376 m/s in the gas medium and 1640 m/s in the liquid. (b) If the pressure amplitudes are equal instead, what is the ratio of the intensities of the waves (of the one in the liquid to that in the gas)?
Answers
Answer:
(a) The ratio of the pressure amplitude of the waves is 43.21
(b) The ratio of the intensities of the waves is 0.000535
Explanation:
Given;
density of gas, [tex]\rho _g[/tex] = 2.27 kg/m³
density of liquid, [tex]\rho _l[/tex] = 972 kg/m³
speed of sound in gas, [tex]C_g[/tex] = 376 m/s
speed of sound in liquid, [tex]C_l[/tex] = 1640 m/s
The of the sound wave is given by;
[tex]I = \frac{P_o^2}{2 \rho C} \\\\P_o^2 = 2 \rho C I\\\\p_o = \sqrt{2 \rho CI}[/tex]
Where;
[tex]P_o[/tex] is the pressure amplitude
[tex]P_o_g= \sqrt{2 \rho _g C_gI} -------(1)\\\\P_o_l= \sqrt{2 \rho _l C_lI}---------(2)\\\\\frac{P_o_l}{P_o_g} = \frac{\sqrt{2 \rho _l C_lI}}{\sqrt{2 \rho _g C_gI}} \\\\\frac{P_o_l}{P_o_g} = \sqrt{\frac{2 \rho _l C_lI}{2 \rho _g C_gI} }\\\\ \frac{P_o_l}{P_o_g} = \sqrt{\frac{ \rho _l C_l}{ \rho _g C_g} }\\\\ \frac{P_o_l}{P_o_g} = \sqrt{\frac{ (972)( 1640)}{ (2.27)( 376)} }\\\\\frac{P_o_l}{P_o_g} = 43.21[/tex]
(b) when the pressure amplitudes are equal, the ratio of the intensities is given as;
[tex]I = \frac{P_o^2}{2 \rho C}\\\\I_g = \frac{P_o^2}{2 \rho _g C_g}-------(1)\\\\I_l = \frac{P_o^2}{2 \rho _l C_l}-------(2)\\\\\frac{I_l}{I_g} = (\frac{P_o^2}{2 \rho _l C_l})*(\frac{2\rho_gC_g}{P_o^2} )\\\\\frac{I_l}{I_g} = \frac{\rho _gC_g}{\rho_lC_l} \\\\\frac{I_l}{I_g} = \frac{(2.27)(376)}{(972)(1640)}\\\\ \frac{I_l}{I_g} = 0.000535[/tex]
Can someone who knows how to do physics please answer this
Answers
Answer:
about 3.17647 hours
Explanation:
The appropriate relation is ...
time = distance/speed
time = (270 km)/(85 km/h) = 3 3/17 h ≈ 3.17647 h
It will take Derek about 3.17647 hours to drive the distance.
is 4x a term? or does it have to remove the 4 to be a term
Answers
Answer:
4x is a term oonly
No need to be romoved
An electromagnet crane is carrying the electromagnet with the help of the three cables. But the electromagnet is not stable because of the wind. What is the reason behind the cause
Answers
Answer:
The reason behind the given instance is summarized below.
Explanation:
When another electromagnet shifts because of the wind, it induces a simulated area that acts on either the electromagnet as an effect or force, considered as the Lorentz force. This force thus renders the resultant force equivalent to a non-zero value mostly on the electromagnet. The balance is not protected by this power. When there is no breeze, just the three connectors sustain equilibrium.15. An astronaut on the moon has a 110 kg crate and a 230 kg crate. How do the forces required to liftyihe crates straight up on the moon compare with the forces required to lift them on Earth?
Answers
Explanation:
Mass of carte 1 is 110 kg and that of crate 2 is 230 kg
Force required to lift crates is equal to its crate i.e. W = mg
On Moon, a = 1.625 m/s²
Weight of crate 1, W = 110 kg × 1.625 m/s² = 178.75 N
Weight of crate 2, W = 230 kg × 1.625 m/s² = 373.75 N
On Earth, g = 9.8 m/s²
Weight of crate 1, W = 110 kg × 9.8 m/s² = 1078 N
Weight of crate 2, W = 230 kg × 9.8 m/s² = 2254 N
Hence, this is the required solution.
The forces required to lift the crates straight up on the Moon is lesser than the forces required to lift them on Earth.
Given the following data:
Mass A = 110 kgMass B = 230 kgScientific data:
Acceleration due to gravity on Earth = 9.8 [tex]m/s^2[/tex]Acceleration due to gravity on Moon = 1.6 [tex]m/s^2[/tex]The formula for weight.Mathematically, the weight of an object is given by the formula;
[tex]Weight = mg[/tex]
Where;
m is the mass of the object.g is the acceleration due to gravity.For the weight on Moon:[tex]Weight \;A= 110 \times 1.6[/tex]
Weight A = 176 Newton.
[tex]Weight \;B=230 \times 1.6[/tex]
Weight B = 368 Newton.
For the weight on Earth:[tex]Weight \;A= 110 \times 9.8[/tex]
Weight A = 1,078 Newton.
[tex]Weight \;B=230 \times 9.8[/tex]
Weight B = 2,254 Newton.
In conclusion, the forces required to lift the crates straight up on the Moon is lesser than the forces required to lift them on Earth.
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URGENT!! A 0.057 kg tennis ball and a tennis racket collide. The racket has an initial
momentum of -2.80 kg m/s and a final momentum of -1.97 kg-m/s. The ball
has an initial momentum of 0.02565 kg-m/s. If you assume the collision is
elastic, what is the final velocity of the ball?
O A. -83.26 m/s
O B. -0.80 m/s
O C. -14.11 m/s
O D. -4.75 m/s
Answers
Answer:
-14.11
Explanation:
Suppose you take a trip that covers 180 km and takes 3 hours to make.
Your average speed is
8. 33 m/s
b. 16.66 m/s
c. 27.78 m/s
d. 41.67 m/s
Answers
Answer:
v = 16,66 m/s
Explanation:
To obtain the velocity of the train we must use the velocity formula for a uniform line movement:
v = x/t
Where x is the space and t is time.
replacing given values:
v = 180 km / 3 h
v = 60 km/h
to pass this value to international units:
v = 60 / 3,6 m/s
v = 16,66 m/s
A body starts with a velocity of 20 m/s, accelerates uniformly for a time t, moves with constant velocity for the same time, and finally decelerates to rest, again taking a time t. Given that the final deceleration is three times the original acceleration, and the total distance travelled is 140 m, find t.
Answers
Answer:
t=0.14s
Explanation:
t=[tex] \frac{s}{v} [/tex]t=[tex] \frac{20}{140} [/tex]Where s= speedV=distance And t=timeWhat effect docs temperature have on the dissolution rate in sugar water?
Answers
You drive 200 miles in 3 hours before stopping
for 30 minutes for lunch and gas. After lunch,
you travel 150 miles in an hour and a half. What
was your average speed for the trip?
Answers
Answer 55.5mph
explanation
If the forces on an object are balanced, the object will do what?
Answers
SOS Physics
Projectile Simulator Lab
Answers
Answer:
i will try out give me some time to solve this
HELP PLSSSSSSSSSjjdndnsnsj
Answers
Answer:
i feel like 3 not too sure tho
8. According to the passage, in order for LeBron James to score a slam-dunk, what must he
exert?
Answers
Answer:
Kenetic Energy?
Explanation:
I need more context of what you are studying here...
Which most likely has the greatest conductivity?
a warm plastic rod
a cool rubber tube
a cool lead metal strip
a warm copper wire
Answers
Answer:
Which most likely has the greatest conductivity?
a warm plastic rod
a cool rubber tube
a cool lead metal stripa warm copper wire
Explanation:
The warm copper wire most likely has the greatest conductivity.
What is conductivity?Conductivity is a measure of how easily a material can conduct electricity. Metals like copper are known for having high electrical conductivity due to the presence of free electrons that can move easily through the material when an electric field is applied.
Non-metallic materials like plastic and rubber generally have low electrical conductivity because they do not have free electrons available for conduction.
Additionally, the temperature of the material can also affect its conductivity. As temperature increases, the movement of atoms and molecules in the material also increases, which can cause a decrease in electrical conductivity.
Therefore, of the materials listed, the warm copper wire is most likely to have the greatest conductivity due to its metallic properties and elevated temperature.
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Please help, Thanks if you do!!! :)
Answers
Answer:
The Elements are arranged from left to right and top to bottom in order of increasing atomic number, and aslo
The arrangement of the periodic table was formulated in order to give a very informative representation of the chemical elements
A 10 kg object has a 40 N force applied to it. What is the acceleration of the object ? *
Answers
Answer:
a = 4 [m/s^2]
Explanation:
To solve this problem we must use Newton's second law, which tells us that force is equal to the product of mass by acceleration.
F = m*a
where:
F = force = 40 [N]
m = mass = 10 [kg]
a = 40/10
a = 4 [m/s^2]
Arctic sea ice has declined over the past few decades causing water levels to increase. This is an interaction of which two spheres? A)Biosphere and geosphere
B)Cryosphere and hydrosphere
C)Geosphere and atmosphere
D)Hydrosphere and geosphere
Answers
Answer:
B
Explanation:
Answer:
Its B)Cryosphere and hydrosphere! I took the test and got that question correct!
Explanation:
A disc with moment of inertia 1.5 kg m2 is rotating with an angular speed of 800 rev/min on a shaft. A second disc, initially at rest and with moment of inertia 5.0 kg m2,is suddenly clamped together to the same shaft.
(a) Determine magnitude of angular momentum of the first disc.
(b) Determine the common angular speed of the combination of the two discs.
Answers
Answer:
Explanation:
Angular momentum p = Iw
I is the moment of inertia
w is the angular velocity
a) Angular momentum of the first disc
p1 = I1w1
Given
I1 = 1.5kg/m²
w1 = 800rev/min
Convert to rad/s
1 rev = 6.283rad
1 min = 60secs
800rev/min = 800(6.283)/60
= 83.77rad/s
p1 = 1.5×83.77
p1 = 125.66kgrad/s
Hence the magnitude of angular momentum of the first disc is 125.66kgrad/s
b) according to law of conservation of momentum
I1w1+I2w2 = (I1+I2)w
w is the common angular speed
Given
11w1 = 125.66
w2 = 0rad/s
I1 = 1.5kgm²
I2 = 5kgm²
Substitute
125.66+0 = (1.5+5)w
125.66 = 6.6w
w = 125.66/6.5
w = 19.33rad/s
Since 1rad/s = 9.549tev/min
19.33rad/s = 184.6rev/min
Hence the common angular speed of the combination of the two discs is 184.6rev/min
A hiker walks 4.30 km east, turns 90.0º due south and walks an additional 2.48 km. What distance did the hiker travel? *
24.64 km
6.78 km
1.82 km
4.96 km
Answers
Answer:
6.78 km
Explanation:
Length of path due east = 4.3km
Length of path south = 2.48km
Unknown:
Distance covered = ?
Solution:
The distance covered is the total length of path from start to finish. It takes cognizance of the turns and every direction moved.
Unlike displacement which only considers the net direction from start to finish, distance sums up the total path.
So;
Distance = 4.3km + 2.48km = 6.78km
Find the force that must be exerted on the rod to maintain a constant current of 0.173 A in the resistor.
Answers
Complete Question
Find the force that must be exerted on the rod to maintain a constant current of 0.173 A in the resistor.
The figure below shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance L = 0.451 m . The rails are connected by a [tex]12.6 \Omega \ resistor[/tex], and the entire system is in a uniform magnetic field with a magnitude of 0.751 T .
The diagram illustrating this question is shown on the first uploaded image
Answer:
The value is [tex]F = 0.0586 \ N [/tex]
Explanation:
From the question we are told that
The current is [tex]I = 0.173 \ A[/tex]
The length of separation is [tex]L= 0.451 \ m[/tex]
The resistance is [tex]12.6 \Omega[/tex]
The magnetic field is [tex]B = 0.751\ T[/tex]
Generally the force is mathematically represented as
[tex]F = BIL sin (\theta )[/tex]
Given that the velocity is perpendicular to magnetic field then [tex]\theta = 90[/tex]
=> [tex]sin(90) = 1[/tex]
So
[tex]F = 0.751 *0.173 * 0.451 sin (\theta )[/tex]
[tex]F = 0.751 *0.173 * 0.451 * 1[/tex]
[tex]F = 0.0586 \ N [/tex]
a dump truck slowly tilts its bed upward to dispose of a 95 kg steel cabinet. For small angle of tilt the crate stay put,but when the tilt angle exceeds 23.2° the steel cabinet begins to slide.What is the coefficient of static friction between the bed of the truck and the steel cabinet?
Answers
Answer:
The value is [tex]\mu =0.4286[/tex]
Explanation:
From the question we are told that
The mass of the steel cabinet is [tex]m = 95 \ kg[/tex]
The threshold angle is [tex]\theta = 23.2^o[/tex]
Generally at the point just before the steel cabinet starts to slide
The horizontal force on the steel cabinet is equal to the frictional force that is
[tex]F_f = F_h[/tex]
Here [tex]F_h[/tex] is the horizontal force which is mathematically represented as
[tex]F_h = m * g cos (theta )[/tex]
and [tex]F_f = \mu N[/tex]
Here N is the normal force acting on the steel cabinet and this is mathematically represented as
[tex]N = mg sin (\theta )[/tex]
=> [tex] m * g cos (theta )= mg sin (\theta ) * \mu [/tex]
=> [tex]\mu = tan (\theta )[/tex]
=> [tex]\mu = tan (23.2)[/tex]
=> [tex]\mu =0.4286[/tex]
The coefficient of static friction between the bed of the truck and steel cabinet is 0.43.
The given parameters;
mass of the steel, m = 95 kgangle of inclination, θ = 23.2⁰The coefficient of static friction between the bed of the truck and steel cabinet is calculated as follows;
[tex]\Sigma F = 0\\\\mg sin(\theta) - \mu mg cos(\theta) = 0\\\\\mu mg cos(\theta ) = mg sin(\theta)\\\\\mu cos(\theta) = sin(\theta)\\\\\mu = \frac{sin(\theta)}{cos(\theta)} \\\\\mu = tan (\theta)\\\\\mu = tan \ (23.2)\\\\\mu = 0.43[/tex]
Thus, the coefficient of static friction between the bed of the truck and steel cabinet is 0.43.
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