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QPages 230-234: Q35: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q35 Solution: Doubly-ionised helium ions are projected with a speed of in a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently mistake the mass of a doubly-ionised helium ion ($\text{He}^{2+}$) for that of a single proton or an electron. You must recognize that the ion retains the nucleus of a helium atom, so its mass is approximately $4m_p$ (where $m_p$ is the proton mass), not $m_p$ or $m_e$.

Doubly-ionised helium ions are projected with a speed of

10 \text{ km s}^{-1}

in a direction perpendicular to a uniform magnetic field of magnitude 1.0 T. Find a) the force acting on an ion b) the radius of the circle in which it circulates and c) the time taken by an ion to complete the circle.

Step-by-Step Verified Solution

**Answer:** (a)

F = 3.2 \times 10^{-15} \text{ N}

(b)

r = 2.08 \times 10^{-4} \text{ m}

(c)

T = 1.31 \times 10^{-7} \text{ s}

. **Step-by-Step Explanation:** (a)

F = q v B = 2 \times 1.6 \times 10^{-19} \times 10^4 \times 1.0 = 3.2 \times 10^{-15} \text{ N}

. (b)

r = \frac{m v}{q B} = \frac{4 \times 1.67 \times 10^{-27} \times 10^4}{2 \times 1.6 \times 10^{-19} \times 1.0} = 2.08 \times 10^{-4} \text{ m}

. (c)

T = \frac{2\pi m}{q B} = 1.31 \times 10^{-7} \text{ s}

.

All Questions in this Chapter

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