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QPages 230-234: Q39: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q39 Solution: A particle of mass and charge is projected into a region that…

A particle of mass mm and charge qq is projected into a region that has a perpendicular magnetic field BB. Find the angle of deviation figure) of the particle as it comes out of the magnetic field if the width dd of the region is very slightly smaller than a) mv/qBmv/qB b) mv/2qBmv/2qB c) 2mv/qB2mv/qB.

Step-by-Step Verified Solution

**Answer:** (a) θ=90∘\theta = 90^\circ (b) θ=30∘\theta = 30^\circ (c) θ=30∘\theta = 30^\circ. **Step-by-Step Explanation:** (a) For d=mv/qBd = mv/qB, the particle just completes a quarter circle: θ=90∘\theta = 90^\circ. (b) For d=mv/2qBd = mv/2qB, sin⁡θ=dr=12⇒θ=30∘\sin\theta = \frac{d}{r} = \frac{1}{2} \Rightarrow \theta = 30^\circ. (c) For d=2mv/qBd = 2mv/qB, the particle exits after θ=30∘\theta = 30^\circ.

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