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sdas [7]
3 years ago
10

Suppose that the current in the solenoid is i(t). The self-inductance L is related to the self-induced EMF E(t) by the equation

E(t)=−Ldi(t)/dt. Find L for a long solenoid with n turns. (Hint: The self-inductance L will always be a positive quantity.), Epxress in μ0, di, dt, R and n
Physics
1 answer:
Artemon [7]3 years ago
4 0

Answer:

L =   μ₀ n r / 2I

Explanation:

This exercise we must relate several equations, let's start writing the voltage in a coil

        E_{L} = - L dI / dt

 

Let's use Faraday's law

       E = - d Ф_B / dt

in the case of the coil this voltage is the same, so we can equal the two relationships

        - d Ф_B / dt = - L dI / dt

The magnetic flux is the sum of the flux in each turn, if there are n turns in the coil

        n d Ф_B = L dI

we can remove the differentials

      n Ф_B = L I

magnetic flux is defined by

     Ф_B = B . A

in this case the direction of the magnetic field is along the coil and the normal direction to the area as well, therefore the scalar product is reduced to the algebraic product

      n B A = L I

the loop area is

      A = π R²

     

we substitute

       n B π R² = L I                    (1)

To find the magnetic field in the coil let's use Ampere's law

        ∫ B. ds = μ₀ I

where B is the magnetic field and s is the current circulation, in the coil the current circulates along the length of the coil

           s = 2π R

we solve

              B 2ππ R =  μ₀ I

              B =  μ₀ I / 2πR

we substitute in

       n ( μ₀ I / 2πR) π R² = L I

       n  μ₀ R / 2 = L I

       L =   μ₀ n r / 2I

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Answer:

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Explanation:

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7 0
3 years ago
A .5kg bird is perched on its nest so that it has 50J of potential energy. how far is it off the of the ground?
pshichka [43]

It is 10.20 m from the ground.

<u>Explanation:</u>

<u>Given:</u>

m = 0.5 kg

PE = 50 J

We know that the Potential energy is calculated by the formula:

P. E = m \times g \times h

where m is the is mass in kg;  g  is acceleration due to gravity which is 9.8 m/s  and  h  is height in meters.

PE is the Potential Energy.

Potential Energy is the amount of energy stored when an object is stationary.

Here, if we substitute the values in the formula, we get

P. E = m \times g \times h

50 = 0.5 × 9.8 × h

50 = 4.9 × h

h = \frac {50} {4.9}

h = 10.20 m

3 0
3 years ago
As air is heated, the particles speed up and spread out (becoming less dense). Hot air balloon pilots can change the balloon’s a
Jobisdone [24]

Answer:

Turn the heater on  

Explanation:

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The downward force is the total weight of the balloon: the air it contains, the gas bag, the basket, the passengers, etc.

The upward force is the weight of the of the air the balloon displaces.

During level flight ,

buoyant force = weight of displaced air - total weight of balloon

If you increase the temperature of the air in the bag, the air molecules spread out and leave through the bottom of the bag.  

The balloon still has the same volume, so the weight of displaced outside air stays the same.

However, the balloon has lost some hot inside air, so its total weight decreases.  

The upward force is greater than the downward force, so the balloon rises.

3 0
3 years ago
A rocket ship is accelerating at 200 m/s2, its mas is 135,000,000 kg. What is the force generated by this acceleration?
Rina8888 [55]

Acceleration does NOT "generate" force.  Acceleration NEEDS force to make it happen.  Without force ... provided by something else ... acceleration can't happen.

The force NEEDED to accelerate a mass with a certain acceleration is

Force needed = (mass) times (acceleration)

For the rocket ship in the question,

Force = (135,000,000 kg) times (200 m/s²)

Force = (135,000,000 x 200) kg-m/s²

<em>Force = 27 Giga-Newtons  </em>(27,000,000,000 Newtons)


The gas-generator cycle F-1 rocket engine, developed in the US by Rocketdyne in the late 1950s, was used in the Saturn V rocket, the main launch vehicle of NASA's Apollo moon lander program .  Five F-1 engines were used in the first stage of each Saturn V.  

==> The thrust of each F-1 engine at full throttle is 7,770 kilo-Newtons.  

It would take <em>3,475 </em>of these F-1 rocket engines, running full-throttle, to provide the force calculated in the answer to this question.  If you didn't have 3,475 F-1 rocket engines, then you couldn't accelerate 135,000,000 kg at 200 m/s².

(And by the way ... the mass of each F-1 engine is 8,400 kg.  So 3,475 engines alone account for 22% of the mass you're trying to accelerate.  And don't even get me started about the mass of the FUEL you'd need to carry.)

5 0
3 years ago
Can i have the physical science grade 12 june 2021 paper (common paper)​
Veseljchak [2.6K]

Answer:

u have to purchase it via online e-commerce platforms

7 0
3 years ago
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