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Artist 52 [7]
3 years ago
11

7. A cube sits in the Cartesian coordinate system. Each side of the cubeis 2m. Electric charge is distributed in the cube with a

density functionV=xy2e2z(C=m3). Find the total charge in the cube
Physics
1 answer:
Zanzabum3 years ago
4 0

Answer:

Net charge inside the cube is 321.6 C

Explanation:

Given charge density function is ρ = xy^2 e^{2z}

side of cube is 2m

According to the definition of volume charge density total charge is given by

q = total charge = \int {\rho} \, dv where dv = dxdydz is the volume element

on substututing the respected values we get

q = \int\limits^2_0 {x} \, dx \int\limits^2_0 {y^2} \, dy \int\limits^2_0 {e^2^z} \, dz  

on solving the above integration we get

q =  \frac{x^2}{2} x \frac{y^3}{3} x \frac{e^2^z}{2}

⇒ q = 321.6 C

Therefore net charge inside the cube is 321.6 C

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A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surfac
Lemur [1.5K]

Answer:

a)   v = 0.9167 m / s,  b)  A = 0.350 m,  c)  v = 0.9167 m / s, d)  A = 0.250 m

Explanation:

a) to find the velocity of the wave let us use the relation

          v = λ f

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           λ = x

           λ = x

the period is the time for the wave to repeat itself, in this case t = 3.00 s corresponds to half a period

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           T = 2t

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           f = 1 / T

           f = 1 / 2t

we substitute

           v = x / 2t

           v = 5.50 / 2 3

           v = 0.9167 m / s

b) the amplitude is the distance from a maximum to zero

          2A = y

           A = y / 2

           A = 0.700 / 2

           A = 0.350 m

c) The horizontal speed of the traveling wave (waves) is independent of the vertical oscillation of the particles, therefore the speed is the same

      v = 0.9167 m / s

d) the amplitude is

           A = 0.500 / 2

           A = 0.250 m

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