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A wire carries a current of 0.89 A. This wire makes an angle of 48° with respect to a magnetic field of magnitude 5.8 x 10-5 T. The wire experiences a magnetic force of magnitude 8.1 x 10-5 N. What is the length of the wire? Number i Units

A wire carries a current of 0.89 A. This wire makes an angle of 48° with respect to a magnetic field of magnitude 5.8 x 10-5 T. The wire experiences a magnetic force of magnitude 8.1 x 10-5 N. What is the length of the wire? Number i Units

College Physics
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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**Problem Statement:** A wire carries a current of 0.89 A. This wire makes an angle of 48° with respect to a magnetic field of magnitude \(5.8 \times 10^{-5}\) T. The wire experiences a magnetic force of magnitude \(8.1 \times 10^{-5}\) N. What is the length of the wire? **Solution:** To solve this, we can use the formula for the magnetic force on a current-carrying wire: \[ F = I \cdot L \cdot B \cdot \sin(\theta) \] Where: - \( F \) is the magnetic force, - \( I \) is the current, - \( L \) is the length of the wire, - \( B \) is the magnetic field, - \( \theta \) is the angle between the wire and the magnetic field. Rearrange the formula to solve for \( L \): \[ L = \frac{F}{I \cdot B \cdot \sin(\theta)} \] Substitute the given values into the formula: \[ L = \frac{8.1 \times 10^{-5}}{0.89 \cdot 5.8 \times 10^{-5} \cdot \sin(48°)} \] After calculating, you will find the length of the wire. Don't forget to input the units once calculated.
Transcribed Image Text:**Problem Statement:** A wire carries a current of 0.89 A. This wire makes an angle of 48° with respect to a magnetic field of magnitude \(5.8 \times 10^{-5}\) T. The wire experiences a magnetic force of magnitude \(8.1 \times 10^{-5}\) N. What is the length of the wire? **Solution:** To solve this, we can use the formula for the magnetic force on a current-carrying wire: \[ F = I \cdot L \cdot B \cdot \sin(\theta) \] Where: - \( F \) is the magnetic force, - \( I \) is the current, - \( L \) is the length of the wire, - \( B \) is the magnetic field, - \( \theta \) is the angle between the wire and the magnetic field. Rearrange the formula to solve for \( L \): \[ L = \frac{F}{I \cdot B \cdot \sin(\theta)} \] Substitute the given values into the formula: \[ L = \frac{8.1 \times 10^{-5}}{0.89 \cdot 5.8 \times 10^{-5} \cdot \sin(48°)} \] After calculating, you will find the length of the wire. Don't forget to input the units once calculated.
Expert Solution
Step 1: Define the given data

The current in the wire is given as i equals 0.89 space A.

The angle of the wire with the magnetic field is theta equals 48 degree.

The magnitude of the magnetic field is B equals 5.8 cross times 10 to the power of negative 5 end exponent space T.

The magnitude of the magnetic force is F equals 8.1 cross times 10 to the power of negative 5 end exponent space N

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