The cube shown in the figure has edge length 2.0 m. There is a non-uniform electric field in the region given by N/C, where a=2.0 and b=2.8. Find the total charge inside the cube. The answer’s unit is pC.

Question

The cube shown in the figure has edge length 2.0 m. There is a non-uniform electric field in the region given by  N/C, where a=2.0 and b=2.8. Find the total charge inside the cube. The answer’s unit is pC.

BlackTom AI · Accepted Answer

The problem asks for the total charge inside a cube given a non-uniform electric field with a specified divergence. First, recall Gauss's law in differential form: Q_enc = ε0 ∭ (∇·E) dV. This means we need the volume integral of the divergence of E over the cube.

From the information, the divergence of the field is constant and equal to a = 2.0 (in units of N/C per meter, effectively the scalar divergence). Since the cube is axis-aligned with edge length L = 2.0 m, its volume is V = L^3 = 8.0 m^3.

Compute the volume integral: ∭ (∇·E) dV = (a) × V = 2.0 × 8.0 = 16.0 (in the appropriate units for flux, i.e., N/C·m^3).

Apply Gauss's law with ε0 = 8.854187817 × 10^-12 F/m: Q_enc = ε0 × ∭ (∇·E) dV = ε0 × 16.0 = 8.854187817e-12 × 16.0 C.

Carrying out the multiplication: 8.854e-12 × 16 ≈ 1.41664e-10 C ≈ 1.42 × 10^-10 C. Converting to picoCoulombs (1 pC = 10^-12 C) gives Q_enc ≈ 142 pC.

Thus, the total charge inside the cube is approximately 142 pC.

The cube shown in the figure has edge length 2.0 m. There is a non-uniform electric field in the region given by N/C, where a=2.0 and b=2.8. Find the total charge inside the cube. The answer’s unit is pC.简答题

类似问题

A point charge q is located at the center of a cube of edge L. What is the flux of the electric field of q through one face of the cube?

Five identical point charges q are located at a distance 2R from the center of a sphere of radius R. The total electric flux through the surface of the sphere is

Using the Divergence Theorem, which of the following is Gauss' Law in differential form? 1) ∇ × 𝐵 → = 1 𝜖 0 𝑞 2) ∇ × 𝐸 → = 1 𝜖 0 𝑞 3) ∇ ∙ 𝐵 → = 1 𝜖 0 𝑞 4) ∇ ∙ 𝐸 → = 1 𝜖 0 𝑞

To derive the equation you used to solve the first part of this question what law did you use?

The cube shown in the figure has edge length 2.1 m. There is a non-uniform electric field in the region given by N/C, where a=2.1 and b=2.0. Find the total charge inside the cube. The answer’s unit is pC.

The cube shown in the figure has edge length 1.6 m. There is a non-uniform electric field in the region given by 𝐸 → = 8 𝑖 ^ + ( 𝑎 𝑦 + 𝑏 ) 𝑗 ^ + 𝑐 𝑘 ^ N/C, where a=2.7 and b=1.6. Find the total charge inside the cube. The answer’s unit is pC.

Consider a spherical Gaussian surface of radius R centered at the origin. A charge Q is placed inside the sphere. To maximize the magnitude of the flux of the electric field through the Gaussian surface, the charge should be located

Which of the following statement about Gauss's law are correct?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单