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natima
11 days 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 [2.2K]11 days 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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20 days ago
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Two very small 8.55-g spheres, 15.0 cm apart from center to center, are charged by adding equal numbers of electrons to each of
ValentinkaMS [2425]

Answer:

1.43 x 10¹⁷.

They will move away from each other.

Explanation:

The force acting on each charged sphere is determined as F = mass x acceleration

= 8.55 x 10⁻³ x 25 x 9.8

= 2.095 N

Assuming Q is the charge on each sphere

F = \frac{9\times10^9\times Q^2}{(15\times10^{-2})^2}

Using the values, 2.095 = \frac{9\times10^9\times Q^2}{(15\times10^{-2})^2}

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The quantity of electrons = Charge / charge of a single electron

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4 0
14 days ago
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Consider the uniform electric field \vec{E} =(4000~\hat{j}+3000~\hat{k})~\text{N/C} ​E ​⃗ ​​ =(4000 ​j ​^ ​​ +3000 ​k ​^ ​​ ) N/
kicyunya [2264]

Answer:

Electric flux is calculated as \phi=31562.63\ Nm^2/C

Explanation:

We start with the given parameters:

The electric field impacting the circular surface is E=(4000j+3000k)\ N/C

Our objective is to ascertain the electric flux passing through a circular region with a radius of 1.83 m situated in the xy-plane. The area vector is oriented in the z direction. The formula for electric flux is expressed as:

\phi=E{\cdot}A

\phi=(4000j+3000k){\cdot}Ak

Applying properties of the dot product, we calculate the electric flux as:

\phi=3000\times Ak

\phi=3000\times \pi (1.83)^2

\phi=31562.63\ Nm^2/C

Consequently, the electric flux for the circular area is \phi=31562.63\ Nm^2/C. Thus, this represents the required answer.

4 0
22 days ago
A bus slows down uniformly from 75.0 km/h to 0 km/h in 21 s. How far does it travel before stopping?
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1 month ago
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inna [2205]

Explanation:

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The graph representing a perfectly inelastic collision is attached, illustrating that both carts move together at the same speed afterward.

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28 days ago
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