A set of wires arranged on the corners of a square of side length \( s \) each carry a different current, as shown in the figure. The wire in the lower left corner carries a constant current \( I \) in the \( \mathbf{k} \)-direction. The wire in the upper left corner carries a current \( \vec{I_1} = -I \mathbf{k} \), the wire in the upper right corner carries a current \( \vec{I_2} = -8I \mathbf{k} \), and the lower right wire carries a current \( \vec{I_3} = \frac{3I}{2} \mathbf{k} \).Determine the vector expression for the net magnetic force \( \frac{\vec{F_B}}{L} \) per unit length \( L \) on the lower left wire using \( \mathbf{ijk} \) unit vector notation. Express your answer in terms of the permeability \( \mu_0 \) of free space, \( s \), \( I \), and numerical constants.\[ \frac{\vec{F_B}}{L} = \text{(Enter your expression here)} \]

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A set of wires arranged on the corners of a square of side length s each carry a different current, as shown in the figure. The wire in the lower left corner carries a constant current I in the k-direction. The wire in the upper left corner carries a current Ì₁ = −I k, the wire in the upper right corner carries a current Ỉ₂ = −81 k, and the lower right wire carries a 1 31 current Ì3 = 2 Determine the vector expression for the net magnetic force FÅ per unit length L on the lower left wire using ijk unit vector notation. Express your answer in terms of the permeability µ of free space, s, I, and numerical constants. 1 L k. ||

A set of wires arranged on the corners of a square of side length s each carry a different current, as shown in the figure. The wire in the lower left corner carries a constant current I in the k-direction. The wire in the upper left corner carries a current Ì₁ = −I k, the wire in the upper right corner carries a current Ỉ₂ = −81 k, and the lower right wire carries a 1 31 current Ì3 = 2 Determine the vector expression for the net magnetic force FÅ per unit length L on the lower left wire using ijk unit vector notation. Express your answer in terms of the permeability µ of free space, s, I, and numerical constants. 1 L k. ||

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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Concept explainers

Electromagnets

The word "electromagnet" is composed of two words, ‘electro’ and ‘magnet’. It is a type of magnet in which an electric current helps in the generation of a magnetic field. Electromagnets usually consist of two major parts, wire and a coil around which the wire is wound. This is called a solenoid. When an electric current is allowed to pass through the coiled wire, the electric current produces a magnetic field. This magnetic field is present only when current is passing through the wire.

Question

A set of wires arranged on the corners of a square of side length \( s \) each carry a different current, as shown in the figure. The wire in the lower left corner carries a constant current \( I \) in the \( \mathbf{k} \)-direction. The wire in the upper left corner carries a current \( \vec{I_1} = -I \mathbf{k} \), the wire in the upper right corner carries a current \( \vec{I_2} = -8I \mathbf{k} \), and the lower right wire carries a current \( \vec{I_3} = \frac{3I}{2} \mathbf{k} \).

Determine the vector expression for the net magnetic force \( \frac{\vec{F_B}}{L} \) per unit length \( L \) on the lower left wire using \( \mathbf{ijk} \) unit vector notation. Express your answer in terms of the permeability \( \mu_0 \) of free space, \( s \), \( I \), and numerical constants.

\[ \frac{\vec{F_B}}{L} = \text{(Enter your expression here)} \]

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