Question

An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true?
a. The electron will be accelerated along the axis.
b. The electron path will be circular about the axis.
c. The electron will experience a force at \(45^{\circ }\) to the axis and hence execute a helical path.
d. The electron will continue to move with uniform velocity along the axis of the solenoid.

• A. c
• B. a
• C. d
• D. b

Hint:

The field inside a solenoid is along its axis, and the force on a charge moving parallel to a field is zero.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Inside a long solenoid the magnetic field is uniform and directed along the axis.

Step 2: Force
The electron moves along the axis, so its velocity is parallel (or antiparallel) to \(\vec{B}\). The force \(\vec{F}=q(\vec{v}\times\vec{B})=0\).

Step 3: Result
With no force the electron neither speeds up nor moves on a circle or helix. It keeps moving with uniform velocity along the axis, which is statement d.

Final Answer:
The electron continues with uniform velocity along the axis. \[ \boxed{\text{(C) }\text{d}} \]