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QPages 249-253: Q59: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q59 Solution: A tightly-wound, long solenoid has turns per unit length, a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly assume the magnetic field inside a solenoid is zero or that the particle moves in a plane, failing to recognize that the field is uniform and axial. The particle executes circular motion in a plane perpendicular to the axis, so the maximum speed is determined by the condition that the cyclotron radius equals the solenoid radius.

A tightly-wound, long solenoid has

n

turns per unit length, a radius

r

and carries a current

i

. A particle having charge

q

and mass

m

is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed for which the particle does not strike the solenoid?

Step-by-Step Verified Solution

**Answer:**

v_{max} = \frac{qBr}{m}

. **Step-BY-Step Explanation:** For the particle to not strike the solenoid, its radius of circular motion must be less than the solenoid radius.

r = \frac{mv}{qB} < r \Rightarrow v < \frac{qBr}{m}

.

All Questions in this Chapter

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