Ch 27: Magnetic Field and Magnetic Forces

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 27: Magnetic Field and Magnetic Forces

Problem 34

Chapter 27, Problem 34

A straight, 2.5 m wire carries a typical household current of 1.5 A (in one direction) at a location where the earth's magnetic field is 0.55 gauss from south to north. Find the magnitude and direction of the force that our planet's magnetic field exerts on this wire if it is oriented so that the current in it is running (a) from west to east, (b) vertically upward, (c) from north to south. (d) Is the magnetic force ever large enough to cause significant effects under normal household conditions?

Verified step by step guidance

To find the force on a current-carrying wire in a magnetic field, use the formula: \( F = I \cdot L \cdot B \cdot \sin(\theta) \), where \( F \) is the force, \( I \) is the current, \( L \) is the length of the wire, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the direction of the current and the magnetic field.

Convert the magnetic field from gauss to tesla. Since 1 gauss = 10^{-4} tesla, the magnetic field \( B = 0.55 \times 10^{-4} \) tesla.

For part (a), the current runs from west to east, and the magnetic field is from south to north. The angle \( \theta \) between the current direction and the magnetic field is 90 degrees, so \( \sin(\theta) = 1 \). Substitute the values into the formula to find the force.

For part (b), the current runs vertically upward, and the magnetic field is horizontal from south to north. Again, the angle \( \theta \) is 90 degrees, so \( \sin(\theta) = 1 \). Use the formula to calculate the force.

For part (c), the current runs from north to south, parallel to the magnetic field. The angle \( \theta \) is 0 degrees, so \( \sin(\theta) = 0 \). Therefore, the force is zero. For part (d), consider the magnitude of the force calculated in parts (a) and (b) to determine if it is significant under normal household conditions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Magnetic Force on a Current-Carrying Wire

The magnetic force on a current-carrying wire is given by the equation F = I(L × B), where I is the current, L is the length vector of the wire, and B is the magnetic field. The force is perpendicular to both the direction of the current and the magnetic field, determined by the right-hand rule. This concept is crucial for calculating the force's magnitude and direction in different orientations of the wire.

Right-Hand Rule

The right-hand rule is a mnemonic for understanding the direction of the magnetic force. To apply it, point your thumb in the direction of the current and your fingers in the direction of the magnetic field; your palm will then face the direction of the force. This rule helps determine the force's direction when the wire is oriented differently relative to the magnetic field.

Earth's Magnetic Field

Earth's magnetic field is a natural magnetic field that extends from the Earth's interior out into space. It is approximately 0.55 gauss at the surface and generally points from the geographic south to the north. Understanding its direction and magnitude is essential for calculating the magnetic force on a wire in various orientations, as it influences the force's direction and strength.

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Textbook Question

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Textbook Question

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Textbook Question

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