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lisabon 2012 [21]
3 years ago
15

A disk with a radius of R is oriented with its normal unit vector at an angle Θ with respect to a uniform electric field. Which

of the following represent the electric flux through the disk?
Physics
2 answers:
marissa [1.9K]3 years ago
8 0

Answer:

The expresion for the flux through the disk is:

Ф = E·πR^2·cos(Θ).

Explanation:

Let's sat the electric field has direction e and the normal to the disk has direction n (bold means vector quantities). So we have:

E=E·e (where E is the magnitud of the electric flied)

A=A·n

The flux for an uniform electric field and a flat surface is:

Ф=E×A

⇒ Ф = E·A·e×n = E·A·cos(angle(e,n)) = E·A·cos(Θ)

Since in this case the area is for a disk of radius R, A=\pi R^{2}

So, Ф = E·πR^2·cos(Θ)

lisabon 2012 [21]3 years ago
3 0

Answer:

The electric flux through the disk are

  • E(πR²)sinϕ
  • E(πR²)cosθ

Explanation:

Electric Force is Calculated by:

Electric flux = E * A cosθ

where

E is the magnitude of the electric field

A represent area of the disk

and θ is the angle between the electric field lines and the normal (perpendicular) to A

Area, A = πR²

So, Electric flux = E(πR²) cosθ

Also, note that the cosine of an angle can be written as sine of its complementary angle.

Assuming θ + ϕ = 180

Then,  cosθ = sinϕ

So, Electric flux = E(πR²) cosθ can be written as

Electric flux = E(πR²) sinϕ

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Complete Question

A commuter train passes a passenger platform at a constant speed of 39.6 m/s. The train horn is sounded at its characteristic frequency of 350 Hz.

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What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding

(b) What wavelength is detected by a person on the platform as the train approaches?

 

Answer:

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  \Delta  f  =  81.93 \ Hz

b

  \lambda_1 =  0.867 \ m

Explanation:

From the question we are told that

      The speed of the train is  v_t  =  39.6 m/s

      The frequency of the train horn is  f_t =  350 \ Hz

Generally the speed of sound has a constant values of  v_s  =  343 m/s

  Now  according to dopplers equation when the train(source) approaches a person on the platform(observe) then the frequency on the sound observed by the observer can be mathematically represented as  

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substituting values

        f_1 =  350 *  \frac{343 }{343-39.6}

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  Now  according to dopplers equation when the train(source) moves away from  the  person on the platform(observe) then the frequency on the sound observed by the observer can be mathematically represented as  

           f_2 =  f *   \frac{v_s}{v_s +v_t}

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        f_2 =  350 *   \frac{343}{343  + 39.6}

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The overall change in frequency is detected by a person on the platform as the train moves from approaching to receding is mathematically evaluated as

        \Delta  f  =  f_1 - f_2

        \Delta  f  =  395.7 - 313.77

        \Delta  f  =  81.93 \ Hz

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          \lambda_1 =  \frac{v}{f_1 }

          \lambda_1 =  \frac{343}{395.7 }

         \lambda_1 =  0.867 \ m

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