Doubly ionized he

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 -