A flat, square surface with side length 3.40 cm is in the x y -plane at z=0 . Calculate the magn

Name: Problem 10, Chapter 27: University Physics with Modern Physics
Uploaded: 2021-01-12T23:43:06-08:00
Duration: 3 min 17 s
Channel: Guilherme Barros
Description: A flat, square surface with side length 3.40 cm is in the x y -plane at z=0 . Calculate the magnitude of the flux through this surface produced by a magnetic field B⃗=(0.200 T) + (0.300 T) Ĵ-(0.500 T) k̂ .

step 1 In this problem, we're going to talk about the magnetic flux. So consider that we have a surface

Question

A flat, square surface with side length 3.40 $\mathrm{cm}$ is in the $x y$ -plane at $z=0 .$ Calculate the magnitude of the flux through this surface produced by a magnetic field $\vec{\boldsymbol{B}}=(0.200 \mathrm{T}) \hat{\boldsymbol{\imath}}+$ $(0.300 \mathrm{T}) \hat{\boldsymbol{J}}-(0.500 \mathrm{T}) \hat{\boldsymbol{k}} .$

   A flat, square surface with side length 3.40 $\mathrm{cm}$ is in the $x y$ -plane at $z=0 .$ Calculate the magnitude of the flux through this surface produced by a magnetic field $\vec{\boldsymbol{B}}=(0.200 \mathrm{T}) \hat{\boldsymbol{\imath}}+$ $(0.300 \mathrm{T}) \hat{\boldsymbol{J}}-(0.500 \mathrm{T}) \hat{\boldsymbol{k}} .$

University Physics with Modern Physics

Hugh D. Young 13th Edition

Chapter 27, Problem 10

Instant Answer

Solved by Expert Guilherme Barros

01/12/2021

Step 1

The vector area A is equal in magnitude to the area of the surface and its direction is perpendicular to the surface. In this case, the surface is a square with side length 3.4 cm, so the magnitude of A is $(3.4 \times 10^{-2} m)^2 = 1.156 \times 10^{-3} m^2$. The Show more…

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A flat, square surface with side length 3.40 $\mathrm{cm}$ is in the $x y$ -plane at $z=0 .$ Calculate the magnitude of the flux through this surface produced by a magnetic field $\vec{\boldsymbol{B}}=(0.200 \mathrm{T}) \hat{\boldsymbol{\imath}}+$ $(0.300 \mathrm{T}) \hat{\boldsymbol{J}}-(0.500 \mathrm{T}) \hat{\boldsymbol{k}} .$

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Key Concepts

Magnetic Flux

Magnetic flux is a measure of the number of magnetic field lines passing through a given area. Mathematically, it is defined as the dot product of the magnetic field vector and the area vector over the surface, which quantifies the effectiveness with which the field permeates the surface.

Area Vector

The area vector is a representation of a surface's magnitude and orientation. For a flat surface, its magnitude is equal to the area of the surface and its direction is perpendicular to the surface. It is crucial in calculating flux since it determines the component of the field contributing to the flux through the surface.

Dot Product

The dot product is a mathematical operation that returns a scalar by multiplying two vectors and incorporating the cosine of the angle between them. In the context of magnetic flux, it is used to calculate the component of the magnetic field that passes through the surface by projecting the field onto the area vector.

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