Question

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

Answer 1

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