Consider a cube with one corner at the origin and with sides of length 50 cm positioned along the x y z axes. There is an electric field E → = < 45, 210 y , 0 > N/C throughout the region that has a constant x component and a y component that increases linearly with y . (Assume the + x axis is to the right, the + y axis is upward, and the + z axis is out of the page. Also assume that the back left corner of the cube is at the origin.)

Charge in the cube = Q = (2.323 × 10⁻¹⁰) C

Explanation:

E → = < 45, 210 y , 0 > N/C

The length of the cube = 50 cm = 0.8 m

To find the charge in the cube, we need the net flux in the cube

In the z-direction, the electric field is 0, no, net flux in that direction,

In the x-direction, the electric field is constant, the same flux thay enters the face at x = 0 is the same that leaves at x= 0

50 cm, hence, no net flux in that direction too.

But the y direction, the electric field changes according to 210y from y = 0 to y = 0.50 m.

At y = 0, electric field = 210(0) = 0 N/C

At y = 0.50, electric field = 210(0.5) = 105 N/C.

Electric flux = Φ = E A = 105 (0.5 × 0.5) = 26.25 Vm or N/m²C

(the area of the xz plane that the field in this direction passes through is indeed 0.5²)

But according to Gauss' law, the net flux in a box is given by

Φ = Q/ε₀

where Q = charge in the box = ?

ε₀ = (8.85 × 10⁻¹²) C²N·m².

Q = Φε₀ = 26.25 × 8.85 × 10⁻¹²

Q = (2.323 × 10⁻¹⁰) C

Hope this Helps!!!

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.