A 7.70-cm length of straight wire runs horizontally along a...

A $7.70-\mathrm{cm}$ length of straight wire runs horizontally along a north-south line. The wire carries a 3.45 - A current flowing northward through a uniform 1.25 -T magnetic field directed vertically upward. Find the magnitude and direction of the magnetic force on the wire.

Key Concepts

Magnetic Force on a Current-Carrying Wire

A wire carrying an electric current experiences a force when placed in a magnetic field. This force is given by the equation F = I(L x B), where I is the current, L is the length (with direction given by the current), and B is the magnetic field. The magnitude of this force depends on the current, the magnitude of the magnetic field, the length of the wire, and the angle between the direction of the current and the magnetic field.

Lorentz Force Law for a Current Element

The Lorentz force law describes how a moving charge or a current element experiences a force in the presence of a magnetic field. For a current-carrying wire, it is the cumulative effect of the forces on all the moving charges in the conductor, leading to the formula F = I(L x B). This law is fundamental in understanding how magnetic fields interact with electrical currents.

Vector Cross Product

The cross product is a vector operation that results in a vector that is perpendicular to the two input vectors. In the context of magnetic force on a wire, taking the cross product of the wire’s length vector (aligned with the current) and the magnetic field vector gives the direction of the resulting force. The magnitude of the cross product is proportional to the sine of the angle between the original vectors.

Right-Hand Rule

The right-hand rule is a simple method used to find the direction of the vector that results from a cross product. When applied to a current-carrying wire in a magnetic field, the rule helps determine that the force is perpendicular to both the current direction and the magnetic field direction. This mnemonic is essential for visualizing the orientation of forces in electromagnetic applications.

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