**Magnetic Flux through a Cube**A cube of edge length $ \ell = 9.0 \, \text{cm} $ is positioned as shown in the figure below. There is a uniform magnetic field throughout the region with components $ B_x = +7.0 \, \text{T} $, $ B_y = +6.0 \, \text{T} $, and $ B_z = +9.0 \, \text{T} $.**Diagram Explanation**The diagram shows a cube with edge length $ \ell $ placed in a three-dimensional coordinate system. The x, y, and z axes are labeled, and the cube is oriented such that one of its faces is parallel to the yz-plane. A vector $\vec{B}$ representing the magnetic field is shown, indicating its three-dimensional nature with components in all three principal directions (x, y, z).**Questions**(a) **Calculate the flux through the shaded face of the cube.**- **Answer Box:** $\Box \, \text{T} \cdot \text{m}^2$(b) **What is the net flux emerging from the volume enclosed by the cube (i.e., the net flux through all six faces)?**- **Answer Box:** $\Box \, \text{T} \cdot \text{m}^2$

(a) The flux through the shaded face of the cube is, ϕB=BAcosθ=Bxl2cosθ Substitute the values.…

Answered: A cube of edge length e = 9.0 cm is…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Magnetic Flux through a Cube**

A cube of edge length $ \ell = 9.0 \, \text{cm} $ is positioned as shown in the figure below. There is a uniform magnetic field throughout the region with components $ B_x = +7.0 \, \text{T} $, $ B_y = +6.0 \, \text{T} $, and $ B_z = +9.0 \, \text{T} $.

**Diagram Explanation**

The diagram shows a cube with edge length $ \ell $ placed in a three-dimensional coordinate system. The x, y, and z axes are labeled, and the cube is oriented such that one of its faces is parallel to the yz-plane. A vector $\vec{B}$ representing the magnetic field is shown, indicating its three-dimensional nature with components in all three principal directions (x, y, z).

**Questions**

(a) **Calculate the flux through the shaded face of the cube.**

- **Answer Box:** $\Box \, \text{T} \cdot \text{m}^2$

(b) **What is the net flux emerging from the volume enclosed by the cube (i.e., the net flux through all six faces)?**

- **Answer Box:** $\Box \, \text{T} \cdot \text{m}^2$

Expert Solution

Step 1

(a)

The flux through the shaded face of the cube is,

$\begin{array}{rcl} ϕ_{B} & = & B A \cos θ \\ = & B_{x} l^{2} \cos θ \end{array}$

Substitute the values.

$\begin{array}{rcl} ϕ_{B} & = & (+ 7.0 T) {[(9.0 cm) (\frac{10^{- 2} m}{1 cm})]}^{2} \cos (0 °) \\ = & (+ 7.0 T) {(9.0 \times 10^{- 2} m)}^{2} \\ = & 0.0567 {T·m}^{2} \end{array}$

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