Question

An electron is projected along the axis of a circular conductor carrying current $I$. The electron will experience

• A. a force along the axis
• B. a force perpendicular to the axis
• C. no force
• D. a force at an angle of $45^\circ$ to the axis

Hint:

A magnetic field can never exert a force on any moving charge if the charge moves parallel or anti-parallel to the field lines ($\vec{v} \parallel \vec{B}$). Since a circular loop's field points strictly along its axis, any charge moving straight down the center passes through completely unaffected.

Answer 1

The Correct Option is C

Step 1: Picture the geometry.
A circular current loop creates a magnetic field, and at every point on its central axis that field points straight along the axis.
Step 2: Note the electron's direction.
The electron is fired along the very same axis, so its velocity $\vec{v}$ is parallel (or anti-parallel) to the field $\vec{B}$ at every point on its path.
Step 3: Recall the magnetic force law.
The force on a moving charge is $$\vec{F} = q\,(\vec{v}\times\vec{B}),\qquad |\vec{F}| = |q|\,v\,B\sin\theta,$$ where $\theta$ is the angle between $\vec{v}$ and $\vec{B}$.
Step 4: Find the angle.
Since $\vec{v}$ and $\vec{B}$ lie along the same line, $\theta = 0^\circ$ or $180^\circ$.
Step 5: Evaluate the sine factor.
Both $\sin 0^\circ$ and $\sin 180^\circ$ equal zero, so $$F = |q|\,v\,B\times 0 = 0.$$
Step 6: Conclude.
A charge moving exactly along the field direction feels no magnetic deflection, so the electron experiences no force.
\[ \boxed{F = 0\ \text{(no force)}} \]