Answer:
Explanation:
Electric flux is defined as the flow of electric field intensity through a given surface.
Mathematically:
![\phi=E.A.cos\ \theta](https://tex.z-dn.net/?f=%5Cphi%3DE.A.cos%5C%20%5Ctheta)
where:
E = electric field
A = area
θ = angle between the area vector and the electric field
Electric flux through the surface of a sphere will be uniform throughout the surface area due to a charge at the center of the sphere. The distance of the surface from the center is always at a constant distance of radius of the sphere.
Electric flux through the surface of a cube will be varying as the surface area is at a varying distance from the center of the cube. The distance of the surface from the center is not at a uniform distance from the center of the cube and so the projection of solid angle changes.
To get x on its own, you times the 3 over to the other side so the 3 cancels out on the LHS.
~ x greater than or equal to -18
(C)
Answer:
F = 3.86 x 10⁻⁶ N
Explanation:
First, we will find the distance between the two particles:
![r = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2}\\](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%2B%28z_%7B2%7D-z_%7B1%7D%29%5E2%7D%5C%5C)
where,
r = distance between the particles = ?
(x₁, y₁, z₁) = (2, 5, 1)
(x₂, y₂, z₂) = (3, 2, 3)
Therefore,
![r = \sqrt{(3-2)^2+(2-5)^2+(3-1)^2}\\r = 3.741\ m\\](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%283-2%29%5E2%2B%282-5%29%5E2%2B%283-1%29%5E2%7D%5C%5Cr%20%3D%203.741%5C%20m%5C%5C)
Now, we will calculate the magnitude of the force between the charges by using Coulomb's Law:
![F = \frac{kq_{1}q_{2}}{r^2}\\](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7Bkq_%7B1%7Dq_%7B2%7D%7D%7Br%5E2%7D%5C%5C)
where,
F = magnitude of force = ?
k = Coulomb's Constant = 9 x 10⁹ Nm²/C²
q₁ = magnitude of first charge = 2 x 10⁻⁸ C
q₂ = magnitude of second charge = 3 x 10⁻⁷ C
r = distance between the charges = 3.741 m
Therefore,
![F = \frac{(9\ x\ 10^9\ Nm^2/C^2)(2\ x\ 10^{-8}\ C)(3\ x\ 10^{-7}\ C)}{(3.741\ m)^2}\\](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B%289%5C%20x%5C%2010%5E9%5C%20Nm%5E2%2FC%5E2%29%282%5C%20x%5C%2010%5E%7B-8%7D%5C%20C%29%283%5C%20x%5C%2010%5E%7B-7%7D%5C%20C%29%7D%7B%283.741%5C%20m%29%5E2%7D%5C%5C)
<u>F = 3.86 x 10⁻⁶ N</u>
Answer:
c = 5 m
Explanation:
this exercise you want to divide the rectangular room into two triangular rooms
the area of triangles is
A = ½ base height
A = ½ 4 3
A = 6 m²
the length of the curtain can be found using the Pythagorean theorem
c² = b² + a²
c = √ (4² + 3²)
c = 5 m
this is the length of the curtain