Q. 434.0( 1 Vote )

Figure shows a convex lens of focal length 12 cm lying in a uniform magnetic field B of magnitude 1.2 T parallel to tis principal axis. A particle having a charge 2.0 × 10–3 C and mass 2.0 × 10–6 kg is projected perpendicular to the plane of the diagram with a speed of 4.8 ms–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 goes along a circle and find the radius of that circle.



Answer :


Given-
Focal length of the convex lens = 12 cm



Uniform magnetic field, B = 1.2 T



Charge of the particle, q = 2.0 × 10−3 C



an mass, m = 2.0 × 10−5 kg



Speed of the particle, v = 4.8 m s−1



Distance between the particle and the lens = 18 cm


Given in the question that the object is projected perpendicularly on the plane of the paper.


The radius of the circular path described by a particle in a magnetic field r,



where,


m is the mass of a proton


v= velocity of the particle


B = magnetic force


q= charge on the particle = C





Given that, the object distance, u = -18 cm



Using the lens formula –



where,


v=distance of image formed from lens


u=distance of the object from lens


f =focal length of the lens


substituting the values-




Let the radius of the circular path of image be r’.



Hence magnification -





Therefore, the radius of the circular path in which the image of the object formed from the lens moves is 8 cm.


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