Answer:
Explanation:
a ) Between r = 0 and r = r₁
Electric field will be zero . It is so because no charge lies in between r = 0 and r = r₁ .
b ) From r = r₁ to r = r₂
At distance r , charge contained in the sphere of radius r
volume charge density x 4/3 π r³
q = Q x r³ / R³
Applying Gauss's law
4πr² E = q / ε₀
4πr² E = Q x r³ / ε₀R³
E= Q x r / (4πε₀R³)
E ∝ r .
c )
Outside of r = r₂
charge contained in the sphere of radius r = Q
Applying Gauss's law
4πr² E = q / ε₀
4πr² E = Q / ε₀
E = Q / 4πε₀r²
E ∝ 1 / r² .
Answer:
<em>➢</em><em>when you crank you make kinetic energy and then the kinetic energy makes potential energy.</em>
Explanation:
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Answer:
Orange , yellow, green and blue
red coat absorbs all colors of visible light except red, so red light
is the only light left to bounce off of the coat toward our eyes.
Answer:
From the question we are told that
The length of the rod is 
The speed is v
The angle made by the rod is 
Generally the x-component of the rod's length is

Generally the length of the rod along the x-axis as seen by the observer, is mathematically defined by the theory of relativity as

=> ![L_xo = [L_o cos (\theta )] \sqrt{1 - \frac{v^2}{c^2} }](https://tex.z-dn.net/?f=L_xo%20%20%3D%20%20%5BL_o%20cos%20%28%5Ctheta%20%29%5D%20%20%5Csqrt%7B1%20%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D)
Generally the y-component of the rods length is mathematically represented as

Generally the length of the rod along the y-axis as seen by the observer, is also equivalent to the actual length of the rod along the y-axis i.e
Generally the resultant length of the rod as seen by the observer is mathematically represented as

=> ![L_r = \sqrt{[ (L_o cos(\theta) [\sqrt{1 - \frac{v^2}{c^2} }\ \ ]^2+ L_o sin(\theta )^2)}](https://tex.z-dn.net/?f=L_r%20%20%3D%20%5Csqrt%7B%5B%20%28L_o%20cos%28%5Ctheta%29%20%5B%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%5C%20%5C%20%5D%5E2%2B%20L_o%20sin%28%5Ctheta%20%29%5E2%29%7D)
=> ![L_r= \sqrt{ (L_o cos(\theta)^2 * [ \sqrt{1 - \frac{v^2}{c^2} } ]^2 + (L_o sin(\theta))^2}](https://tex.z-dn.net/?f=L_r%3D%20%5Csqrt%7B%20%28L_o%20cos%28%5Ctheta%29%5E2%20%2A%20%5B%20%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%5D%5E2%20%2B%20%28L_o%20sin%28%5Ctheta%29%29%5E2%7D)
=> ![L_r = \sqrt{(L_o cos(\theta) ^2 [1 - \frac{v^2}{c^2} ] +(L_o sin(\theta))^2}](https://tex.z-dn.net/?f=L_r%20%20%3D%20%5Csqrt%7B%28L_o%20cos%28%5Ctheta%29%20%5E2%20%5B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%5D%20%2B%28L_o%20sin%28%5Ctheta%29%29%5E2%7D)
=> ![L_r = \sqrt{L_o^2 * cos^2(\theta) [1 - \frac{v^2 }{c^2} ]+ L_o^2 * sin(\theta)^2}](https://tex.z-dn.net/?f=L_r%20%3D%20%20%5Csqrt%7BL_o%5E2%20%2A%20cos%5E2%28%5Ctheta%29%20%20%5B1%20-%20%5Cfrac%7Bv%5E2%20%7D%7Bc%5E2%7D%20%5D%2B%20L_o%5E2%20%2A%20sin%28%5Ctheta%29%5E2%7D)
=> ![L_r = \sqrt{ [cos^2\theta +sin^2\theta ]- \frac{v^2 }{c^2}cos^2 \theta }](https://tex.z-dn.net/?f=L_r%20%20%3D%20%20%5Csqrt%7B%20%5Bcos%5E2%5Ctheta%20%2Bsin%5E2%5Ctheta%20%5D-%20%5Cfrac%7Bv%5E2%20%7D%7Bc%5E2%7Dcos%5E2%20%5Ctheta%20%7D)
=> 
Hence the length of the rod as measured by a stationary observer is

Generally the angle made is mathematically represented

=> 
=>
Explanation: