(II) A long wire stretches along the x axis and carries a 3.0-A current to the right (+x) . The

step 1 So we don't have the length given in the problem, but we do know the direction of the length. So

(II) A long wire stretches along the x axis and carries a...

(II) A long wire stretches along the $x$ axis and carries a $3.0-\mathrm{A}$ current to the right $(+x) .$ The wire is in a uniform magnetic field $\vec{\mathbf{B}}=(0.20 \hat{\mathbf{i}}-0.36 \hat{\mathbf{j}}+0.25 \hat{\mathbf{k}}) \mathrm{T}$ . Determine the components of the force on the wire per cm of length.

(II) A long wire stretches along the $x$ axis and carries a $3.0-\mathrm{A}$
current to the right $(+x) .$ The wire is in a uniform
magnetic field $\vec{\mathbf{B}}=(0.20 \hat{\mathbf{i}}-0.36 \hat{\mathbf{j}}+0.25 \hat{\mathbf{k}}) \mathrm{T}$ . Determine
the components of the force on the wire per cm of length.

Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept refers to the force experienced by a conductor when it carries an electric current in a magnetic field. The physical mechanism is explained by the Lorentz force, which acts on the moving charges inside the conductor, and is given by F = I (L × B), where I is the current, L is a vector representing the direction and length of the current element, and B is the magnetic field. This formula shows that both the magnitude and the direction of the force depend on the current as well as the orientation of the conductor relative to the magnetic field.

Vector Cross Product

The cross product is a mathematical operation used to determine the direction and magnitude of the force on the current element in a magnetic field. In the context of electromagnetism, it yields a vector that is perpendicular to both the current direction and the magnetic field, following the right-hand rule. This operation is fundamental for accurately calculating the resulting force's components when dealing with three-dimensional vector fields.

Force per Unit Length

This concept involves expressing the total force experienced by an extended object, like a current-carrying wire, in terms of the force acting on a unit length of the conductor. It simplifies the analysis by normalizing the force over the wire's length, making it easier to apply the results to wires of various lengths in uniform magnetic fields.

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