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natima
3 months ago
10

Consider the uniform electric field E = (2.5 j + 3.5 k) × 103 N/C. (a) Calculate the electric flux through a circular area of ra

dius 2.5 m that lies in the yz-plane. Give your answer in N·m2/C. b) Repeat the electric flux calculation for the circular area for the case when its area vector is directed at 45° above the xy-plane. Give your answer in N·m2/C.
Physics
1 answer:
kicyunya [3.2K]3 months ago
3 0
The desired electric flux Φ is calculated from the electric field E=(2.5• j + 3.5• k) ×10³ N/C and a circular path with a radius r=2.5m. The electric flux across a surface is represented as Φ=∮E•dA. Given the area A lies in the yz-plane, the normal orientation flows in the x-direction with A=πr² leading to dA=2πrdr •i. Thus, Φ evolves to Φ=∮(2.5j + 3.5k)×10³•(2πrdr i). Integrating from r=0 to r=2.5m and noting that components in different directions yield zero, results in Φ equaling 0 Nm²/C. Regarding the second part, when the area vector is at a 45° angle to the xy-plane, we redefine dA as (2πrCos45 i + 2πrSin45 j) dr, leading to the new flux calculation as Φ=10³∮ 5πrSin45 dr, integrating from 0 to 2.5m. With substitutions made, the result comes to Φ=34.71×10³ Nm²/C.
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The reaction force is F = -8 N. It is noted that the Earth's gravitational force pulls the toy down with a weight of 8.0 N. This problem utilizes Newton's third law of motion, which states that "for every action, there is an equal and opposite reaction." In a mathematical context, it is illustrated as follows: where the force exerted on one object by another is indicated. In this scenario, the force of Earth acting on the toy is the action force. Consequently, the reaction force is characterized as F = -8 N (the negative indicates that the reaction force is directed upward). In essence, the toy exerts an upward force of 8 N on the Earth, thus comprising the required solution.
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2 months ago
When a charge is placed on a metal sphere, it ends up in equilibrium at the outer surface. Use this information to determine the
Maru [3345]

Answer:

a

The value at a point inside is Zero

b

The electric field is E = 2.7*10^{6} \ N/C

Explanation:

We know from the problem that

The charge magnitude is q = 3.0 \mu C = 3.0 *10^{-6} \ C

The radius of the spherical ball is r = 5.0 \ mm = 0.005 \ m

According to Gauss’s law, the enclosed charge within a conductor is zero which indicates that the electric field within the spherical ball is zero

On the outside, the electric field around the spherical ball is mathematically expressed as

E = \frac{kq}{ a^2}

Here a denotes a point outside the spherical ball with its value of a = 10 \ cm = \frac{10}{100} = 0.1 \ m

and k represents Coulomb's constant, valued at

k = 9*10^{9}\ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}.

=> E = \frac{ 3 *10^{-6} * 9*10^9 }{ (0.1)^2}

=> E = 2.7*10^{6} \ N/C

5 0
2 months ago
A skateboarder is attempting to make a circular arc of radius r = 16 m in a parking lot. The total mass of the skateboard and sk
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To address this question, we will utilize concepts linked to centripetal force, aligning it with the static frictional force acting on the object. Using this relationship, we can derive the velocity and input the known values. The defined values are:

r = 16m

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\mu_s = 0.63

The maximum velocity can be determined using centripetal force,

F_c = \frac{mv^2}{r}

Should be equal to,

\frac{mv^2}{r} = \mu_s mg

v = \sqrt{\mu_s gr}

v = \sqrt{(0.63)(9.8)(16)}

v = 9.93m/s

As a result, the highest speed achievable through the arc without slipping is 9.93m/s

3 0
3 months ago
In an isolated system, the total heat given off by warmer substances equals the total heat energy gained by cooler substances. N
Keith_Richards [3271]

Answer:

The temperature of the cooler object was nearly at room temperature. As a result, the system underwent minimal change

Explanation:

In a closed system with two objects at varying temperatures, heat energy typically flows from the hotter object to the cooler one. This transfer is more pronounced when there is a significant temperature disparity between the objects. Conversely, if the temperature difference is minor or negligible, the resulting change will be minimal.

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2 months ago
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1 meter per second converts to 2.237 miles per hour

therefore, 83 m/sec is equal to 185.666 miles per hour!!...here is the answer!!

6 0
4 months ago
Read 2 more answers
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