Q. 35

# Doubly ionized helium ions are projected with a speed of 10 km s^{–1} in a direction perpendicular to a uniform magnetic field of magnitude 1.0 T. Find

(a) the force acting on an ion,

(b) the radius of the circle in which it circulates and

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

Answer :

Given-

Speed of the helium ions, *v* = 10 km s^{−1} = 10^{4} m/s

Uniform magnetic field, *B* = 1.0 T

Charge on the helium ions = 2*e*

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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