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28. Magnetic Fields and Forces

Summary of Magnetism Problems

Physics

28. Magnetic Fields and Forces

Summary of Magnetism Problems

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3:59 minutes

Problem 83

Textbook Question

An airplane has acquired a net charge of 1160 μC. If the Earth’s magnetic field of 5.0 x 10^-5 T is perpendicular to the airplane’s velocity of magnitude 120 m/s, determine the force on the airplane.

Verified step by step guidance

Identify the formula to calculate the magnetic force on a charged object moving through a magnetic field: \( F = qvB \sin(\theta) \), where \( F \) is the magnetic force, \( q \) is the charge, \( v \) is the velocity, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the velocity and the magnetic field.

Substitute the given values into the formula. The charge \( q = 1160 \mu C = 1160 \times 10^{-6} \, C \), the velocity \( v = 120 \, m/s \), the magnetic field strength \( B = 5.0 \times 10^{-5} \, T \), and since the magnetic field is perpendicular to the velocity, \( \sin(\theta) = \sin(90^\circ) = 1 \).

Simplify the formula by substituting \( \sin(90^\circ) = 1 \), so the equation becomes \( F = qvB \).

Multiply the values of \( q \), \( v \), and \( B \) to calculate the magnetic force. Ensure the units are consistent (Coulombs for charge, meters per second for velocity, and Tesla for magnetic field).

The result of the multiplication will give the magnitude of the magnetic force \( F \) acting on the airplane in Newtons.

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Key Concepts

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

Coulomb's Law

Coulomb's Law describes the force between two charged objects. The force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. In this context, it helps understand how the airplane's charge interacts with other charges in its vicinity, although the primary focus here is on the magnetic force.

Magnetic Force on a Charged Particle

The magnetic force acting on a charged particle moving in a magnetic field is given by the equation F = q(v × B), where F is the force, q is the charge, v is the velocity of the particle, and B is the magnetic field. This force is perpendicular to both the velocity of the charge and the magnetic field, which is crucial for determining the direction and magnitude of the force on the airplane.

Lorentz Force

The Lorentz force is the combined effect of electric and magnetic forces on a charged particle. In this scenario, since only the magnetic field is mentioned, the Lorentz force simplifies to the magnetic force equation. Understanding this concept is essential for calculating the force acting on the airplane due to its charge and the Earth's magnetic field.

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