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The figure below shows tracks of three charged particles in a uniform electrostatic field. Which particle has the highest charge to the mass ratio?

A

2

B

3

C

1

D

1 and 3

Step-by-Step Solution

The vertical deflection yy of a charged particle moving perpendicularly into a uniform electric field is given by y=12at2y = \frac{1}{2} a t^2. Since a=qEma = \frac{qE}{m} and t=xvxt = \frac{x}{v_x}, the deflection is y=qEx22mvx2y = \frac{qE x^2}{2m v_x^2}. This shows that the deflection yy is directly proportional to the charge-to-mass ratio (qm\frac{q}{m}), assuming the initial velocity and horizontal distance are comparable. From the figure (NCERT Physics Class 12, Fig 1.30), particle 3 suffers the maximum deflection, indicating it has the highest magnitude of charge to mass ratio. (See NCERT Physics Class 12, Exercise 1.13).

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