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QPages 230-234: Q43: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q43 Solution: The figure shows a convex lens of focal length 12 cm lying in a …

The figure shows a convex lens of focal length 12 cm lying in a uniform magnetic field BB of magnitude 1.2 T parallel to its principal axis. A particle with charge 2.0×10−3 C2.0 \times 10^{-3} \text{ C} and mass 2.0×10−5 kg2.0 \times 10^{-5} \text{ kg} is projected perpendicular to the plane of the diagram with a speed of 4.8 m s−14.8 \text{ m s}^{-1}. The particle moves along a circle with its centre on the principal axis at a distance of 18 cm from the lens. Show that the image of the particle moves along a circle and find the radius of that circle.

Step-by-Step Verified Solution

**Answer:** Radius of image circle =1.2 cm= 1.2 \text{ cm}. **Step-by-Step Explanation:** The particle moves in a circle of radius r=mvqB=2×10−5×4.82×10−3×1.2=0.04 m=4 cmr = \frac{m v}{q B} = \frac{2 \times 10^{-5} \times 4.8}{2 \times 10^{-3} \times 1.2} = 0.04 \text{ m} = 4 \text{ cm}. The lens forms an image of this circular motion. Using the lens formula, the image is a circle of radius 1.2 cm1.2 \text{ cm}.

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