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5. (Problem 22-23) A wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of 0.390 T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (a) 60.0°, (b) 90.0°, and (c) 120°.

5. (Problem 22-23) A wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of 0.390 T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (a) 60.0°, (b) 90.0°, and (c) 120°.

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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5. Please assist with this question with details on how to do it. Thank you 

**Problem Description:** A wire of length 2.80 meters carries a current of 5.00 amperes in a region where a uniform magnetic field has a magnitude of 0.390 teslas. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is: - (a) 60.0 degrees - (b) 90.0 degrees - (c) 120.0 degrees **Approach to Solution:** Use the formula for the magnetic force \( F \) on a current-carrying wire: \[ F = I \cdot L \cdot B \cdot \sin(\theta) \] where: - \( I \) is the current (5.00 A), - \( L \) is the length of the wire (2.80 m), - \( B \) is the magnetic field strength (0.390 T), - \( \theta \) is the angle between the wire and the magnetic field. **Steps to Calculate:** 1. **Case (a):** Angle \( \theta = 60.0^\circ \) - Calculate \( \sin(60.0^\circ) \). - Substitute into the formula to find \( F \). 2. **Case (b):** Angle \( \theta = 90.0^\circ \) - Calculate \( \sin(90.0^\circ) \). - Substitute into the formula to find \( F \). 3. **Case (c):** Angle \( \theta = 120.0^\circ \) - Calculate \( \sin(120.0^\circ) \). - Substitute into the formula to find \( F \). This problem helps in understanding the impact of the angle between the direction of current and magnetic field on the magnitude of the magnetic force experienced by the wire.
Transcribed Image Text:**Problem Description:** A wire of length 2.80 meters carries a current of 5.00 amperes in a region where a uniform magnetic field has a magnitude of 0.390 teslas. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is: - (a) 60.0 degrees - (b) 90.0 degrees - (c) 120.0 degrees **Approach to Solution:** Use the formula for the magnetic force \( F \) on a current-carrying wire: \[ F = I \cdot L \cdot B \cdot \sin(\theta) \] where: - \( I \) is the current (5.00 A), - \( L \) is the length of the wire (2.80 m), - \( B \) is the magnetic field strength (0.390 T), - \( \theta \) is the angle between the wire and the magnetic field. **Steps to Calculate:** 1. **Case (a):** Angle \( \theta = 60.0^\circ \) - Calculate \( \sin(60.0^\circ) \). - Substitute into the formula to find \( F \). 2. **Case (b):** Angle \( \theta = 90.0^\circ \) - Calculate \( \sin(90.0^\circ) \). - Substitute into the formula to find \( F \). 3. **Case (c):** Angle \( \theta = 120.0^\circ \) - Calculate \( \sin(120.0^\circ) \). - Substitute into the formula to find \( F \). This problem helps in understanding the impact of the angle between the direction of current and magnetic field on the magnitude of the magnetic force experienced by the wire.
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