Charge is accelerated from rest through a potential difference VVV and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius RRR. If the accelerating potential is tripled to 3VVV, what will be the radius of the circular arc?

The radius of the circular arc is √3 R

Explanation:

Centripetal force is Balanced by magnetic force

mv² / r = qvB

==> r = mv / qB (1)

By conservation of energy

1/2mv² = qv

v = √2qv/m(2)

substituting in equation (2) in equation (1)

r = m/qB x √2qv/m

r = ( √2mv/q) B

radius is proportional to voltage

r ∝ √v₂

r₂/r₁ = √v₂/v₁

r₂ = R x √3v/v

r₂ = √3 R

thermal energy is the answer

the rearrangement of particles in a physical change. hope this