In other words a infinitesimal segment dV caries the charge
<span>dQ = ρ dV </span>
<span>Let dV be a spherical shell between between r and (r + dr): </span>
<span>dV = (4π/3)·( (r + dr)² - r³ ) </span>
<span>= (4π/3)·( r³ + 3·r²·dr + 3·r·(dr)² + /dr)³ - r³ ) </span>
<span>= (4π/3)·( 3·r²·dr + 3·r·(dr)² + /dr)³ ) </span>
<span>drop higher order terms </span>
<span>= 4·π·r²·dr </span>
<span>To get total charge integrate over the whole volume of your object, i.e. </span>
<span>from ri to ra: </span>
<span>Q = ∫ dQ = ∫ ρ dV </span>
<span>= ∫ri→ra { (b/r)·4·π·r² } dr </span>
<span>= ∫ri→ra { 4·π·b·r } dr </span>
<span>= 2·π·b·( ra² - ri² ) </span>
<span>With given parameters: </span>
<span>Q = 2·π · 3µC/m²·( (6cm)² - (4cm)² ) </span>
<span>= 2·π · 3×10⁻⁶C/m²·( (6×10⁻²m)² - (4×10⁻²m)² ) </span>
<span>= 3.77×10⁻⁸C </span>
<span>= 37.7nC</span>
Answer:
Heyyy hope this helps
Convection currents describe the rising, spread, and sinking of gas, liquid, or molten material caused by the application of heat.
Answer:
The angle between the blue beam and the red beam in the acrylic block is

Explanation:
From the question we are told that
The refractive index of the transparent acrylic plastic for blue light is 
The wavelength of the blue light is 
The refractive index of the transparent acrylic plastic for red light is 
The wavelength of the red light is 
The incidence angle is 
Generally from Snell's law the angle of refraction of the blue light in the acrylic block is mathematically represented as
![r_F = sin ^{-1}[\frac{sin(i) * n_a }{n_F} ]](https://tex.z-dn.net/?f=r_F%20%3D%20%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bsin%28i%29%20%2A%20%20n_a%20%7D%7Bn_F%7D%20%5D)
Where
is the refractive index of air which have a value of
So
![r_F = sin ^{-1}[\frac{sin(45) * 1 }{ 1.497} ]](https://tex.z-dn.net/?f=r_F%20%3D%20%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bsin%2845%29%20%2A%20%201%20%7D%7B%201.497%7D%20%5D)

Generally from Snell's law the angle of refraction of the red light in the acrylic block is mathematically represented as
![r_C = sin ^{-1}[\frac{sin(i) * n_a }{n_C} ]](https://tex.z-dn.net/?f=r_C%20%3D%20%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bsin%28i%29%20%2A%20%20n_a%20%7D%7Bn_C%7D%20%5D)
Where
is the refractive index of air which have a value of
So
![r_C = sin ^{-1}[\frac{sin(45) * 1 }{ 1.488} ]](https://tex.z-dn.net/?f=r_C%20%3D%20%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bsin%2845%29%20%2A%20%201%20%7D%7B%201.488%7D%20%5D)

The angle between the blue beam and the red beam in the acrylic block

substituting values

