Answered: You have two single turn circular loops…

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

You have two single turn circular loops of wire oriented such that they have a common center and the planes of the loops are perpendicular. As shown in the figure below, loop #1 lies in the in the xy-plane and has a counterclockwise current when viewed from the positive z-axis, while loop #2 lies in the xz-plane and has a counterclockwise current when viewed from the positive y-axis.

(a) If the loops each have a radius of 3.3 cm and they each carry a current of 3.1 A, determine the magnitude of the net magnetic field at the common center.
T

(b) The direction of a vector in three dimensions is often given by the angle it makes with the positive x, y, and z-axes. What is the angle between the net magnetic field at the center and the positive x-axis?
°

What is the angle between the net magnetic field at the center and the positive y-axis?
°

What is the angle between the net magnetic field at the center and the positive z-axis?
°

**Transcription for Educational Website:**

**Description of the Setup:**

You have two single-turn circular loops of wire oriented such that they have a common center, and the planes of the loops are perpendicular. As illustrated in the figure, loop #1 lies in the xy-plane and has a counterclockwise current when viewed from the positive z-axis, while loop #2 lies in the xz-plane and has a counterclockwise current when viewed from the positive y-axis.

**Diagram Explanation:**

The diagram shows two perpendicular circular loops.
- Loop #1, positioned in the xy-plane, carries a current I1, with a counterclockwise direction from the positive z-axis perspective.
- Loop #2 is in the xz-plane with a current I2, counterclockwise from the positive y-axis viewpoint.
- The loops intersect at their common center (origin).
- The diagram has a three-axis reference frame labeled x, y, and z.

**Questions and Problems:**

(a) If the loops each have a radius of 3.3 cm and they each carry a current of 3.1 A, determine the magnitude of the net magnetic field at the common center.

[Input Box] T

(b) The direction of a vector in three dimensions is often given by the angle it makes with the positive x, y, and z-axes. What is the angle between the net magnetic field at the center and the positive x-axis?

[Input Box] °

What is the angle between the net magnetic field at the center and the positive y-axis?

[Input Box] °

**Question:**

What is the angle between the net magnetic field at the center and the positive z-axis?

**Input Field:**

A box to enter the angle value, followed by the degree symbol (°).

This question prompts learners to calculate or estimate the angle formed between a magnetic field and an axis in a given setup, often applicable in physics studies related to electromagnetism.

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