Answered: What magnetic flux ΦB does the sensor…

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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Question

An engineer tests a new magnetic flux sensor consisting of a two‑dimensional square membrane, 4.30 cm on each side. The sensor measures the magnetic flux through the membrane. The engineer places the sensor so that it is parallel to and 3.30 cm3.30 cm above the x⁢y-plane in the field region. The edges of the sensor are aligned to the positive x- and y-axes. The normal vector for the sensor's surface points straight up, parallel to the z-axis.

To test the new sensor, the engineer sets up a region of magnetic field. The magnetic vector field is described by

B→=(0.0220⁢ T·cm⁻³)⁢x^2⁢y⁢ı^+(0.0600⁢ T·cm⁻²)⁢x⁢y⁢ȷ^−(0.388⁢ T·cm⁻³)⁢x⁢y²⁢k^

What magnetic flux ΦB does the sensor measure?

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