Answer :

Given-


Speed of the helium ions, v = 10 km s−1 = 104 m/s


Uniform magnetic field, B = 1.0 T


Charge on the helium ions = 2e


Mass of a helium ion, m = 4×1.6×10-27 Kg


(a) The force acting on an ion –


Magnetic force, we know, Lorentz force F is given by -



where,


e = charge on an electron


v = velocity of the electron


B=magnetic field


θ= angle between B and v








(b) The radius of the circle is given by,



where,


m is the mass of a proton


v= velocity of the particle


B = magnetic force


q= charge on the particle





(c) The time taken by an ion to complete the circle,


we know





Since the total time taken for a complete cycle will be its circumference and the velocity is V -





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