A horizontal power line carries a current of 7000 A from...

A horizontal power line carries a current of 7000 A from south to north. Earth's magnetic field $(60.0 \mu \mathrm{T})$ is directed toward the north and inclined downward at $70.0^{\circ}$ to the horizontal. Find the (a) magnitude and (b) direction of the magnetic force on $100 \mathrm{~m}$ of the line due to Earth's field. Assuming $B_{x}=0$, find (a) the magnitude $E$ and (b) $B$ in unit-vector notation.

A horizontal power line carries a current of 7000 A from south to north. Earth's magnetic field $(60.0 \mu \mathrm{T})$ is directed toward the north and inclined downward at $70.0^{\circ}$ to the horizontal. Find the (a) magnitude and (b) direction of the magnetic force on $100 \mathrm{~m}$ of the line due to Earth's field. Assuming $B_{x}=0$, find
(a) the magnitude $E$ and (b) $B$ in unit-vector notation.

Key Concepts

Magnetic Force on a Current-Carrying Conductor

This principle is encapsulated in the equation F = I L x B, which states that a conductor of length L carrying a current I, when placed in a magnetic field B, experiences a force that is proportional to the current, the length, and the sine of the angle between the current and the magnetic field. Understanding this concept is fundamental in electromagnetism as it explains how electric currents interact with magnetic fields to produce mechanical forces.

Magnetic Field Vector Components

Magnetic fields are vector quantities that have both magnitude and direction and can be decomposed into horizontal and vertical components. Decomposing the field is crucial when the field is inclined or has multiple components, as it allows for the analysis of how each component interacts with other vectors in a physical problem.

Cross Product and Right-Hand Rule

The cross product is a mathematical operation on two vectors that results in a new vector perpendicular to the plane formed by the original vectors. In electromagnetism, the right-hand rule is used to determine the direction of the resulting force vector when calculating the cross product, ensuring that the relationship between the current direction and the magnetic field is correctly represented.

Unit Vector Notation

Unit vector notation provides a way to express vectors by decomposing them into components along the standard basis directions, typically denoted as i, j, and k. This notation is essential for clearly representing both the magnitude and direction of vectors in a concise and standardized form, making it easier to perform and communicate vector calculations in physics.

Transcript

Please give Ace some feedback