Along the x Axis A wire 50 cm long lying along the x axis carries a current of 0.50 A in the p

Step 1: First, we need to convert the length of the wire from cm to m. So, $50 mathrm{~cm} = 0.5

Along the x Axis A wire 50 cm long lying along the x axis...

Along the $x$ Axis A wire $50 \mathrm{~cm}$ long lying along the $x$ axis carries a current of $0.50 \mathrm{~A}$ in the positive $x$ direction. It passes through a magnetic field $\vec{B}=(0.0030 \mathrm{~T}) \hat{\mathrm{j}}+(0.0100 \mathrm{~T}) \hat{\mathrm{k}} .$ Find the magnetic force on the wire.

Key Concepts

Vector Components

Vectors in three-dimensional space are typically expressed in terms of their components along the x, y, and z coordinate axes, often represented by unit vectors i, j, and k. This component form simplifies the process of performing vector operations, such as addition, subtraction, and the cross product, by allowing each component to be handled individually. Understanding vector components is crucial for analyzing and solving problems involving forces and fields in physics.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the resultant vector when taking the cross product of two vectors. In the context of electromagnetic force calculations, it involves pointing the fingers of the right hand in the direction of the current (or the first vector), curling them toward the direction of the magnetic field (or the second vector), with the thumb then indicating the direction of the force. This method ensures that the orientation of the force is correctly established.

Magnetic Force on a Current-Carrying Conductor

A current-carrying conductor in a magnetic field experiences a force that is determined by the vector cross product of the current direction and the magnetic field. This force is calculated using the equation F = I (L × B), where I represents the current, L is the vector length of the conductor in the direction of the current flow, and B is the magnetic field. The magnitude and direction of this force depend on the angle between the conductor and the magnetic field, and it is a fundamental concept in the study of electromagnetism.

Vector Cross Product

The vector cross product is an operation performed on two vectors in three-dimensional space that produces a new vector, which is perpendicular to both of the original vectors. This operation is essential for calculating forces in electromagnetic contexts because it helps determine both the magnitude and direction of the force. The magnitude of the cross product is given by the product of the magnitudes of the two vectors and the sine of the angle between them, and its direction is determined by the right-hand rule.

Please give Ace some feedback