Ask question

Ask question

All categories

miss Akunina [59]

3 years ago

7

A cubical shell with edges of length a is positioned so that two adjacent sides of one face are coincident with the +x and +y ax

es of a rectangular coordinate system and the corner formed by these two sides is at the origin. An electric field of magnitude E=bx2 directed along the +x axis exists in this region.
1.How much charge is contained in the volume of the shell?
2.Express your answer in terms of the variables a, b, and the permittivity constant ϵ0.

1 answer:

fomenos3 years ago

3 0

Answer: Q = ba⁴ * ε₀

Explanation:

Remember, Gauss's Law states that:

"The net electric flux through any hypothetical closed surface is equal to 1/ε₀ times the net electric charge within that closed surface" i.e

flux Φ = Q / ε₀ where

ε₀ = 8.85e-12 C²/N·m²

Also, the flux, Φ = EAcosθ, where

E = magnitude of the electric field in V/m

A = area of the surface in m²

θ = angle between the electric field lines and the normal (perpendicular) to S.

The field is directed along the x-axis, so all of the flux passes through the side of the cube at x = a. This means that θ = 0º. Thus,

Φ = EA

Then, E = bx² and we're interested in the point where x = a, so if we substitute x for a, we have

E = ba²

Since A = a² for the cube face, we have

Q / ε₀ = ba² * a²

so

Q = ba⁴ * ε₀

You might be interested in

Why does heat cause a substance to expand?

natita [175]

Middle school? lol but, the third one.

5 0

2 years ago

In a typically constructed research study, the experimental group is selected:

blondinia [14]

Answer:

D. from a separate pool than is the control group.

Explanation:

in the picture the person answers is backwards but...

hope this helps have a nice day

7 0

1 year ago

g An object with mass m=2 kg is completely submerged, and tethered, to the bottom of a large body of water. If the density of th

Anit [1.1K]

Answer:

The tension in the rope is 20 N

Solution:

As per the question:

Mass of the object, M = 2 kg

Density of water, $\rho_{w} = 1000\ kg/m^{3}$

Density of the object, $\rho_{ob} = 500\kg/m^{3}$

Acceleration due to gravity, g = $10\ m/s^{2}$

Now,

From the fig.1:

'N' represents the Bouyant force and T represents tension in the rope.

Suppose, the volume of the block be V:

V = $\frac{M}{\rho_{ob}}$ (1)

Also, we know that Bouyant force is given by:

$N = \rho_{w}Vg$

Using eqn (1):

$N = \rho_{w}\frac{M}{\rho_{ob}}g$

$N = 1000\frac{2}{500}\times 10 = 40\ N$

From the fig.1:

N = Mg + T

40 = 2(10) + T

T = 40 - 20 = 20 N

$N = \rho_{w}Vg$

3 0

3 years ago

An airplane is flying at an elevation of 5150 ft, directly above a straight highway. two motorists are driving cars on the highw

docker41 [41]

Using trigonometric ratios we can get the distance;
For the first car; The distance from the point on the highway below the plane
tan = opp/adj
tan(36°) = 5150/x
0.727 = 5150/x
0.727x = 5150
x = 7088.37
For the second car we also use tangent; the distance from the point on the highway below the plane will be;
tan(56°) = 5150/y
1.483 = 5150/y
1.483y = 5150
y= 3473.72
The we can add the two distances to get how far apart the cars are;
7088.37 + 3473.72 = 10562.09 feet.
= 10562.09 ft

7 0

3 years ago

Hi, I'm having a lot of trouble with this one. The answer I got to was 407.91 but I'm not confident in it.

Alecsey [184]

Answer:

6.20×10⁴ V/m

Explanation:

The magnitude of electric field is:

E = √(Eₓ² + Eᵧ²)

where Eₓ = ∂φ/∂x and Eᵧ = ∂φ/∂y.

φ = 1.11 (x² + y²)^-½ − 429x

Eₓ = -0.555 (x² + y²)^-(³/₂) (2x) − 429

Eᵧ = -0.555 (x² + y²)^-(³/₂) (2y)

Evaluating at (0.003, 0.003):

Eₓ = -44034 V/m

Eᵧ = -43605 V/m

The magnitude is:

E = 61971 V/m

Rounded to three significant figures, the strength of the electric field is 6.20×10⁴ V/m.

3 0

3 years ago