A current-carrying conductor placed in a magnetic field experiences the greatest force when the direction of c

Question

A current-carrying conductor placed in a magnetic field experiences the greatest force when the direction of current is:

Examoogle · Accepted Answer

The correct answer is Option C: Perpendicular to the magnetic field. A current-carrying conductor experiences a magnetic force defined by the Lorentz force law. The magnitude of this force is directly proportional to the sine of the angle between the conductor's current direction and the magnetic field vector.

Step-by-Step Solution & Concepts:
A current-carrying conductor experiences a magnetic force defined by the Lorentz force law. The magnitude of this force is directly proportional to the sine of the angle between the conductor's current direction and the magnetic field vector.

Working Principle: The magnetic force $F$ is calculated using the cross product of the current vector $I\vec{L}$ and the magnetic field vector $\vec{B}$, given by $F = I L B \sin(	heta)$. When $	heta = 90^\circ$, $\sin(90^\circ) = 1$, which represents the maximum value for the sine function, leading to the greatest force.

Key Formulas: $F = I L B \sin(	heta)$ — Magnitude of magnetic force on a current-carrying wire

Key Points: Force is zero when the conductor is parallel ($	heta = 0^\circ$) or anti-parallel ($	heta = 180^\circ$) to the field.; Force is maximum when the conductor is perpendicular ($	heta = 90^\circ$) to the magnetic field.; The direction of the force is determined by Fleming's Left-Hand Rule.

Applications: Electric motors; Loudspeakers; Galvanometers

Additional Info: The SI unit of magnetic field strength $B$ is the Tesla ($T$).. Option A and D result in zero force because $\sin(0^\circ) = 0$ and $\sin(180^\circ) = 0$.

Answer: C is correct — The magnetic force is proportional to $\sin(	heta)$, which reaches its maximum value of $1$ when $	heta = 90^\circ$.

Exam Tip: Always remember that in physics problems involving vector cross products, the maximum result occurs at $90^\circ$, while the minimum (zero) occurs at $0^\circ$ or $180^\circ$.

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Option A: Parallel to the magnetic field

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Option B: At an angle of 45 degrees to the field

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Option D: Anti-parallel to the magnetic field

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