a What is the speed of the particle ms b What is the magnitu

(a) What is the speed of the ?-particle?
____________m/s

(b) What is the magnitude of the magnetic force on it?
_____________ N

(c) What is the radius of its circular path?
_____________m

Solution

(a)
From the definition of p.d.
p.d. = W_D / coul = E_k/coul
where, E_k = kinetic energy
E_k = 1.12 * 10⁶ * 2e = 1.792 x 10^-13 J
E_k = 1/2 mv^2
v = sqrt(2*E_k/m) = sqrt(2 x 1.792 x 10^-13 / 6.64 x 10^-27)
v = 7.35 x 10⁶ m/s

(b)
F = q (v x B)
For mutually orthogonal, v x B = vB
F = 2 x 1.6 x 10^-19 x 7.35 x 10⁶ x 1.8
F = 4.232 x 10^-12 N

(c)
particle costrained to move in circle if its velolicty is in same plane as B
centripetal force, F = m*v^2/r (from part b)
which is equal to magnetic force
r = m*v^2/F
r = 2 * E_k / F
r = 2 x 1.792 x 10^-13 J / 4.232 x 10^-12 N
r = 0.085 m