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An electron is projected with uniform velocity along the axis of current carrying long solenoid. Which of the following is true?

Asked in GUJCET 2023 · Lorentz force and work done

• (1) The electron path will be circular about the axis.
• (2) The electron will be accelerated along the axis.
• (3) The electron will experience a force at 45° to the axis and hence execute a helical path.
• (4) The electron will continue to move with uniform velocity along the axis of the solenoid.

Step-by-step solution

Why the other options are wrong

• (1) A circular path needs the velocity perpendicular to ⃗B. Inside the solenoid ⃗B lies along the axis and so does ⃗v, so there is no perpendicular component to bend into a circle.
• (2) A magnetic force is never directed along ⃗B, so it cannot accelerate the electron along the axis — and here it is zero in any case.
• (3) The force is not merely at some angle to the axis, it is exactly zero: ⃗v×⃗B=0 when ⃗v and ⃗B are parallel. With no force there is nothing to wind the path into a helix.

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