<h2>The flux through the infinite charged wire along the central axis of a cylindrical surface of radius r and length l is ∅E = E x 2πrl </h2>
Explanation:
let us consider a thin infinitely long straight wire having a uniform charge density λ Cm⁻¹.To determine the field at a distance r from the line charge , we have cylindrical gaussian surface of radius r, length l,and with its axis along the line charge. it has curved surface S₁ , and flat circular ends S₂ and S₃. Obviously, dS₁//E, dS₂ ⊥E , and dS₃ ⊥ E , so, only the curved surface contributes towards the total flux.
∅E = ∫ E.dS = ∫E.dS₁ +∫E.dS₂ +∫E.dS₃
= ∫EdS₁ cos0⁰ +∫EdS₂ cos 90⁰ +∫Eds₃ cos 90⁰
= E∫ds₁₁ +0+0
= E x area of curved surface
∅E = E x 2πrl
The peak wavelength of Betelgeuse is 828 nm
Explanation:
The relationship between surface temperature and peak wavelength of a star is given by Wien's displacement law:

where
is the peak wavelength
T is the surface temperature
is Wien's constant
For Betelgeuse, the surface temperature is approximately
T = 3500 K
Therefore, its peak wavelength is:

Learn more about wavelength:
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PART A)
Electrostatic potential at the position of origin is given by

here we have



now we have


Now work done to move another charge from infinite to origin is given by

here we will have

so there is no work required to move an electron from infinite to origin
PART B)
Initial potential energy of electron




Now we know



now by energy conservation we will have
So here initial total energy is sufficient high to reach the origin
PART C)
It will reach the origin