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28. Magnetic Fields and Forces

Circular Motion of Charges in Magnetic Fields

Physics

28. Magnetic Fields and Forces

Circular Motion of Charges in Magnetic Fields

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5:20 minutes

Problem 41

Textbook Question

A circular coil 18.0 cm in diameter and containing twelve loops lies flat on the ground. The Earth’s magnetic field at this location has magnitude 5.50 x 10⁻⁵ T and points into the Earth at an angle of 54.0° below a line pointing due north. If a 7.10-A clockwise current passes through the coil, (a) determine the torque on the coil; (b) which edge of the coil rises up : north, east, south, or west?

Verified step by step guidance

Step 1: Calculate the area of the circular coil. The diameter of the coil is given as 18.0 cm, so the radius is half of that. Use the formula for the area of a circle: A = πr², where r is the radius of the coil. Convert the radius to meters before substituting into the formula.

Step 2: Determine the magnetic moment of the coil. The magnetic moment (μ) is given by the formula μ = NIA, where N is the number of loops (12), I is the current (7.10 A), and A is the area of the coil calculated in Step 1.

Step 3: Calculate the torque on the coil. The torque (τ) is given by the formula τ = μBsinθ, where μ is the magnetic moment from Step 2, B is the Earth's magnetic field (5.50 × 10⁻⁵ T), and θ is the angle between the magnetic moment and the magnetic field (54.0°).

Step 4: Analyze the direction of the torque to determine which edge of the coil rises. Use the right-hand rule: point your fingers in the direction of the current in the coil (clockwise when viewed from above), and curl them in the direction of the magnetic field. The thumb will point in the direction of the torque, indicating which edge of the coil rises.

Step 5: Conclude which edge of the coil rises based on the torque direction. Consider the orientation of the coil (flat on the ground) and the direction of the Earth's magnetic field (pointing into the Earth at an angle). This will help determine whether the north, east, south, or west edge rises.

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Key Concepts

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

Torque in Magnetic Fields

Torque in a magnetic field is the rotational force experienced by a current-carrying coil placed in the field. It is calculated using the formula τ = n * I * A * B * sin(θ), where τ is torque, n is the number of loops, I is the current, A is the area of the coil, B is the magnetic field strength, and θ is the angle between the magnetic field and the normal to the coil's surface.

Magnetic Field Direction

The direction of the magnetic field is crucial for determining the behavior of the coil. In this scenario, the Earth's magnetic field points into the Earth at an angle, which affects the torque direction and the resulting motion of the coil. The right-hand rule can be used to visualize the interaction between the current direction and the magnetic field.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the torque and the magnetic force on a current-carrying conductor. By pointing the thumb of the right hand in the direction of the current and curling the fingers in the direction of the magnetic field, the palm indicates the direction of the force or torque acting on the coil. This rule is essential for predicting the coil's rotational movement.

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