In Fig. 30-10, the magnetic field is up out of the page and...

In Fig. $30-10$, the magnetic field is up out of the page and $B=0.80$ T. The wire shown carries a current of 30 A. Find the magnitude and direction of the force on a $5.0 \mathrm{~cm}$ length of the wire. Fig. $30-10$ We know that $\Delta F_{M}=I(\Delta L) B \sin \theta=(30 \mathrm{~A})(0.050 \mathrm{~m})(0.80 \mathrm{~T})(1)=1.2 \mathrm{~N}$ By the right-hand rule, the force is perpendicular to both the wire and the field and is directed toward the bottom of the page.

In Fig. $30-10$, the magnetic field is up out of the page and $B=0.80$
T. The wire shown carries a current of 30 A. Find the magnitude and direction of the force on a $5.0 \mathrm{~cm}$ length of the wire.
Fig. $30-10$
We know that
$\Delta F_{M}=I(\Delta L) B \sin \theta=(30 \mathrm{~A})(0.050 \mathrm{~m})(0.80 \mathrm{~T})(1)=1.2 \mathrm{~N}$
By the right-hand rule, the force is perpendicular to both the wire and the field and is directed toward the bottom of the page.

Key Concepts

Right-Hand Rule

The right-hand rule is a standard mnemonic in physics used to determine the direction of the magnetic force acting on a current-carrying conductor. By pointing your right-hand thumb in the direction of the current and your fingers in the direction of the magnetic field, your palm will face in the direction of the force, providing an intuitive way to visualize the three-dimensional interactions between current, magnetic field, and force.

Magnetic Force on a Current-Carrying Conductor

This concept explains that a current-carrying wire placed in a magnetic field experiences a force. The magnitude of this force is given by the equation F = I L B sin?, where I is the current, L is the length of the wire, B is the magnetic field strength, and ? is the angle between the direction of the current and the magnetic field. It is a fundamental principle in electromagnetism that shows how electric currents interact with magnetic fields.

Cross Product and Sine Function

The use of the cross product in vector mathematics is essential for calculating the magnetic force. In the formula, the cross product inherently accounts for both the magnitude and the direction of the force, with the sine of the angle (sin?) reflecting how the effectiveness of the force depends on the orientation of the wire relative to the magnetic field. Maximum force is obtained when the current and magnetic field are perpendicular to each other.

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