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A charged particle with initial velocity is placed in regions with different field configurations. Match each situation (List-I) with the type of path (List-II). List-I: (P) E = 0, B not zero; initial velocity perpendicular to B. (Q) E not zero, B = 0; initial velocity perpendicular to E. (R) E not zero, B not zero, E parallel to B; initial velocity perpendicular to both E and B. (S) E not zero, B not zero, E perpendicular to B; initial velocity perpendicular to both E and B and magnitude = E/B. List-II: (1) Straight line (2) Parabola (3) Circular (4) Helical with non-uniform pitch (5) Helical with uniform pitch
- P-3, Q-2, R-5, S-1
- P-3, Q-2, R-4, S-1
- P-3, Q-2, R-5, S-2
- P-3, Q-2, R-4, S-2
Correct answer: P-3, Q-2, R-4, S-1
Solution
P: E=0, B not zero, v perp B. Magnetic force F=qv*B provides centripetal acceleration. Particle moves in a circle (3). Q: E not zero, B=0, v perp E. Constant force perpendicular to initial velocity: parabolic path (2). R: E parallel to B, v perp to both. The component of v along B is initially zero. E accelerates particle along B, increasing the axial speed each revolution. The helical pitch (= v_axial * period) keeps increasing: non-uniform pitch (4). S: E perp B, magnitude of initial velocity = E/B, direction perp to both. Electric force (qE upward) and magnetic force (qvB downward) cancel. Net force = 0: straight line (1). Answer: P-3, Q-2, R-4, S-1.
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