A thin 1.00 m long copper rod in a uniform magnetic field...

A thin $1.00 \mathrm{m}$ long copper rod in a uniform magnetic field has a mass of $50.0 \mathrm{g}$. When the rod carries a current of $0.245 \mathrm{A}$, it floats in the magnetic field. What is the field strength of the magnetic field?

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Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept refers to the force exerted on a conductor carrying an electric current when it is placed in an external magnetic field. The magnitude of this force is given by the formula F = I L B, where I is the current, L is the length of the conductor in the magnetic field, and B is the field strength. The direction of the force is determined by the right-hand rule, making it perpendicular both to the direction of the current and the magnetic field.

Gravitational Force

This is the force by which the Earth attracts objects towards its center. It is calculated as F = mg, where m is the mass of the object and g is the acceleration due to gravity. In problems like this, gravitational force is often compared with other forces to determine conditions for equilibrium.

Equilibrium Condition in a Force Balance

In scenarios where an object is floating or at rest in a field, the net force must be zero. This means that all the upward forces, such as the magnetic force in this case, balance all the downward forces, like the gravitational force. By setting these forces equal, one can solve for unknown parameters, such as the magnetic field strength.

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