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makkiz [27]
3 years ago
12

A coaxial cable consists of alternating coaxial cylinders of conducting and insulating material. Coaxial cabling is the primary

type of cabling used by the cable television industry and is also widely used for computer networks such as Ethernet, on account of its superior ability to transmit large volumes of the electrical signals with minimum distortion. Like all other kinds of cables, however, coaxial cables also have some self-inductance that has undesirable effects, such as producing some distortion and heating. Consider a long coaxial cable made of two coaxial cylindrical conductors that carry equal currents I in opposite directions (see figure). The inner cylinder is a small solid conductor of radius a. The outer cylinder is a thin-walled conductor of outer radius b, electrically insulated from the inner conductor. Calculate the inductance per unit length Ll of this coaxial cable.

Physics
1 answer:
kkurt [141]3 years ago
6 0

Answer:

inductance per unit length is  \frac{L}{l} = \frac{\mu_o}{2 \pi} ln (\frac{b}{a} )

Explanation:

   The diagram of coaxial cable is shown on the first uploaded image

From the question we are told that

      The radius of the inner conductor is  a

       The current passing through the first cylindrical conductors is  = I

      The current passing through the first cylindrical conductors is = - I

      The radius of the outer conductor is  b

According to Ampere's law

          ∮ (\= B \ \= dl) = \mu_o  I

=>       B (2 \pi r) = \mu_o I

=>      B  = \frac{\mu_o I }{2 \pi r }      

   The magnetic flux on the coaxial cable can be mathematically represented as

            \phi = \int\limits^{r_2}_{r_1} {\= B \cdot \= da} \, dx  

          \phi = \int\limits^{\frac{b}{2} }_{\frac{a}{2} } {   \frac{\mu_o I }{2 \pi r }  * l *  dr } \,  

        \phi =    \frac{\mu_o I \ * \ l  }{2 \pi r } [ln [\frac{b}{2} - ln [\frac{a}{2} ] ]]  

        \phi =    \frac{\mu_o I \ * \ l  }{2 \pi r }  ln [\frac{b}{a} ]  

Now the emf induced in the coaxial cable is mathematically represented as

            \epsilon = \frac{d \phi }{dt}  = L \frac{dI}{dt}

=>             \frac{d \phi }{dt}  = L \frac{dI}{dt}

=>            \int\limits {\phi} \,    = L \int\limits {dI} \,

=>            \phi = L I

substituting for  \phi

               \frac{\mu_o I \ * \ l  }{2 \pi r }  ln [\frac{b}{a} ] =  LI

dividing through by l

         \frac{L}{l} = \frac{\mu_o}{2 \pi} ln (\frac{b}{a} )

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(b) The distance of mass from mass A if there is no gravitational force acted on C
shepuryov [24]

Answer:

(a) The force, acting on object 'C' is approximately 2.66972 × 10⁻¹⁰ Newtons

(b) The distance of 'C' from 'A', in the direction particle 'B' if there is no  meters gravitational force acting on 'C' is appromimately 0.829 meters or 1.877 meters

Explanation:

The given parameters are;

The mass of particle, A, m₁ = 2 kg

The mass of particle, B, m₂ = 0.3 kg

The mass of particle, C, m₃ = 0.05 kg

The distance between particle 'A' and particle 'B', r₁ = 0.15 m

The distance between particle 'B' and particle 'C', r₂ = 0.05 m

(a) The gravitational force, 'F', is given as follows;

F =G \times \dfrac{m_{1} \times m_{2}}{r^{2}}

Where;

F = The force between the two masses

G = The gravitation constant = 6.67430 × 10⁻¹¹ N·m²/kg²

m₁ = The mass of object 1

m₂ = The mass of object 2

If 'C' is placed at 0.05 m from 'B', we have;

F₂₃ =  6.67430 × 10⁻¹¹ × 0.05 × 0.3/(0.05²) ≈ 4.00458 × 10⁻¹⁰

The gravitational force between force between particle 'B' and particle 'C', F₂₃ = 4.00458 × 10⁻¹⁰ N (towards the right)

F₁₃ =  6.67430 × 10⁻¹¹ × 0.05 × 2/(0.1²) ≈ × 10⁻¹⁰

The gravitational force between force between particle 'A' and particle 'B', F₁₃ = 6.6743 × 10⁻¹⁰ N (towards the left)

The force, 'F', acting on object 'C' = F₁₃ - F₂₃

F = (6.6743 - 4.00458) × 10⁻¹⁰ = 2.66972 × 10⁻¹⁰ N

The force, acting on object 'C' ≈ 2.66972 × 10⁻¹⁰ N

(b), When there is no gravitational force acting on 'C', let the distance of 'C' from 'A' = x

We have;

F₂₃ = F₁₂

F_{23} =G \times \dfrac{m_{1} \times m_{2}}{r_1^{2}} = F_{13} =G \times \dfrac{m_{1} \times m_{3}}{r_2^{2}}

By plugging in the values and removing like terms, we get;

\dfrac{0.3 \times 0.05}{(1.15 - x)^{2}}  = \dfrac{2 \times 0.05}{x^2}

(1.15 - x)² × 2 × 0.05 = 0.3 × 0.05 × x²

0.1·x² - 0.23·x + 1.3225 = 0.015·x²

0.1·x² - 0.23·x + 1.3225 - 0.015·x² = 0

0.085·x² - 0.23·x + 0.13225= 0

x = (0.23± √((-0.23)² - 4 × 0.085 × ( 0.13225)))/(2 × 0.085))

x ≈ 0.829, or x ≈ 1.877

Therefore, the distance of 'C' from 'A', if there is no gravitational force acting on 'C', x ≈ 0.829 m, or x = 1.877 m, in the direction of 'B'

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CAN SOMEONE PLEASE HELP ME
s2008m [1.1K]
The answer should be B
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If you are given force and distance, you can determine power if you know (2 points)
dangina [55]

Answer:

The answer is time

Explanation:

So when youre given force and distance, you can determine work done

Work Done = Force × Distance travelled in the

direction of the force

Since Power = Work Done/ Time

when you know work done, and you want to find power, you will need time.

Because you have work done already, you dont need energy. Though you can use energy and time to find work too. The alternative formula for Power would be:

Power = Energy Converted/Time

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What was Galileo’s contribution to the study of motion?
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Before giving you the answer straight away, I’d like to make sure you understand each option.


FIRST OPTION


“He developed the three laws of motion."


This option is not only the incorrect answer, but it is an incorrect statement. Galileo did not develop the three laws of motion. Isaac Newton was the one to compiled the three laws of motion.


SECOND OPTION


“He was the first to systematically study force and motion."


This option is a statement is true, and it could also be the correct answer. Galileo Galilei used experiments to search for the cause of motion.


THIRD OPTION


“He was the first to discover gravity."


This option is not only the incorrect answer, but it is an incorrect statement. Galileo was not the person to discover gravity. Sir Isaac Newton was the first to discover gravity.


FINAL OPTION


“He improved on Newton's laws."


This option is not only the incorrect answer, but it is an incorrect statement. Galilei did not improve Sir Isaac Newton’s laws.


Now that we’ve gone through each of the options individually, we can go ahead and determine the correct answer to the question, which is...


B ) He was the first to systematically study force and motion.



- Marlon Nunez

8 0
3 years ago
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