A wire 50.0 cm long carries a 0.500 A current in the positive direction of an x axis through a

step 1 In this question, we are given a wire that is 50 cm long, then there's a current that is moving

A wire 50.0 cm long carries a 0.500 A current in the...

A wire $50.0 \mathrm{~cm}$ long carries a $0.500 \mathrm{~A}$ current in the positive direction of an $x$ axis through a magnetic field $\vec{B}=$ $(3.00 \mathrm{mT}) \hat{\mathrm{j}}+(10.0 \mathrm{mT}) \mathrm{k}$. In unit-vector notation, what is the magnetic force on the wire?

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Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept explains that a current-carrying wire in a magnetic field experiences a force whose magnitude and direction depend on the current, the length of the wire, and the magnetic field. The force is described by the equation F = I(L × B), where I is the current, L is the length vector in the direction of the current, and B is the magnetic field vector.

Vector Cross Product

The cross product is a mathematical operation on two vectors that results in a third vector perpendicular to the plane defined by the original vectors. Its magnitude is given by the product of the magnitudes of the two vectors times the sine of the angle between them, and its direction is determined by the right-hand rule, which is essential in finding the direction of the magnetic force.

Unit Vector Notation

Unit vector notation is used in physics to express vectors in terms of their direction along the coordinate axes. This method simplifies the representation of vectors in three-dimensional space by indicating their components along the standard basis vectors, commonly denoted as i, j, and k, which correspond to the x, y, and z axes respectively.

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