Verified Solution • 2025–26 Session moderate

QPages 230-234: Q49: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q49 Solution: A particle with a charge of 5.0 _C and a mass of is projected…

A particle with a charge of 5.0 _C and a mass of 5.0×10−12 kg5.0 \times 10^{-12} \text{ kg} is projected with a speed of 1.0 km s−11.0 \text{ km s}^{-1} in a magnetic field of magnitude 5.0 mT. The angle between the magnetic field and the velocity is sin⁡−10.90)\sin^{-1}0.90). Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch.

Step-by-Step Verified Solution

**Answer:** Diameter =2.9 cm= 2.9 \text{ cm}, Pitch =1.6 cm= 1.6 \text{ cm}. **Step-by-Step Explanation:** The velocity component perpendicular to the field is v⊥=vsin⁡θv_\perp = v \sin\theta, and parallel is v∥=vcos⁡θv_\parallel = v \cos\theta. r=mv⊥qB=1.45 cmr = \frac{m v_\perp}{q B} = 1.45 \text{ cm}. Diameter =2r=2.9 cm= 2r = 2.9 \text{ cm}. p=v∥T=vcos⁡θ×2πmqB=1.6 cmp = v_\parallel T = v \cos\theta \times \frac{2\pi m}{q B} = 1.6 \text{ cm}.

All Questions in this Chapter

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