Question

A positive charge enters a magnetic field and travels parallel to but opposite the field. The charge feels or experiences

• A. an upward force
• B. a downward force
• C. an accelerative force
• D. no force

Hint:

The magnetic force on a charged particle is zero when its velocity is parallel to the magnetic field.

Answer 1

The Correct Option is D

The magnetic force on a moving charge is given by:

\[ F = q(\vec{v} \times \vec{B}) \] where \( q \) is the charge, \( \vec{v} \) is the velocity of the charge, and \( \vec{B} \) is the magnetic field. This force is dependent on the angle between the velocity vector (\( \vec{v} \)) and the magnetic field vector (\( \vec{B} \)), as indicated by the cross product in the equation. When the charge is moving parallel to and opposite the magnetic field, the angle between \( \vec{v} \) and \( \vec{B} \) is 0°, meaning the sine of this angle, \( \sin(0^\circ) \), is zero.

Since the force is proportional to the cross product of the two vectors, the force is zero when the vectors are either parallel or antiparallel. In this case, the charge does not experience any magnetic force because the velocity vector and the magnetic field vector do not create a perpendicular component to generate a force.

Thus, the magnetic force acting on the charge is zero in this situation, confirming that the correct answer is (d).