Un segmento de cable de 1,0 m de longitud se encuentra a lo largo del eje x y lleva una corrien

Step 1: Determine the direction of the magnetic fieldu000Au000AGiven that the magnetic field is given by

Un segmento de cable de 1,0 m de longitud se encuentra a lo...

Un segmento de cable de $1,0 \mathrm{~m}$ de longitud se encuentra a lo largo del eje $x y$ lleva una corriente de 2,0 A en la dirección $x$ positiva. Alrededor del cable está el campo magnético de $(3,0 \hat{\mathbf{i}} \times 4,0 \hat{\mathbf{k}}) \times 10^{-3} \mathrm{~T}$. Halle la fuerza magnética en este segmento.

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the resultant vector in a cross product operation, such as when finding the magnetic force on a wire. By pointing the fingers of the right hand in the direction of the first vector (current direction) and curling them towards the second vector (magnetic field), the thumb then points in the direction of the force. This rule is essential in understanding and predicting the orientation of forces in electromagnetic systems.

Vector Cross Product

The vector cross product is an operation that takes two vectors and returns a third vector that is perpendicular to both. Its magnitude is given by the product of the magnitudes of the two original vectors and the sine of the angle between them. In applications like calculating the magnetic force on a current element, the cross product is used to determine both the direction and magnitude of the resulting force.

Lorentz Force on a Current-Carrying Conductor

This concept describes how a current-carrying wire placed in a magnetic field experiences a force. The force is given by the equation F = I (L × B), where I is the current, L is the vector representing the segment of the wire, and B is the magnetic field. It encapsulates the interaction between electrical currents and magnetic fields, a fundamental principle in electromagnetism.

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