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Problem 1 - Olympiad

A circular coil of radius R carries a current I in a clockwise direction. An electron is moving with velocity v parallel to the axis of the coil at a point on the axis at distance z (z >> R) from the center. What is the direction of the magnetic force on the electron?

Correct: D

Using Biot-Savart law, the magnetic field at a large distance (z >> R) from the center of the coil along the axis can be approximated as a dipole field. The field direction at the axis of a clockwise current loop points into the page (using right-hand thumb rule). Since the electron is moving along the axis, its velocity is parallel to the magnetic field lines. The magnetic force on a charge is given by F = q(v × B). When the velocity and magnetic field are parallel, the cross product is zero. Hence, the force on the electron is zero.