Circular Motion In a Magnetic Field See Figure 3. A particle of charge +4e and m

Question

Circular Motion In a Magnetic Field See Figure 3. A particle of charge +4e and mass m is accelerated from rest by a potential difference V. The particle then enters a region of uniform magnetic field B perpendicular to the velocity. The particle will undergo uniform circular motion. If, instead, the charge is doubled and the mass is quadrupled, while keeping both the potential difference and strength of the magnetic field the same, (i) how does the radius of orbit now compare to the original (give a ratio), (ii) how does the frequency of orbit now compare to the original, and lastly, (iii) how does the kinetic energy nov compare to the original?

Explanation / Answer

for circular motion in magnetic field

qvB=mv^2/r

qB=mv/r

mv=rqB

let charge is q and mass is m

then qV=0.5mv^2

v=sqrt(2qV/m)

r=mv/qB=(1/B)*sqrt(2Vm/q)

if charge is doubled and mass is duadrabled

new r=sqrt(2) times the initial r

(b)f=v/2pi*r=qB/2*pi*m

so frequency will be half

(c) kinetic energy=qV

so it will be 2 times

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