# In terms of rp, determine the radius rd of the circular orbit for the deuteron.

A proton (charge +e, mass mp), a deuteron (charge +e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference ΔV. Each of the particles enters a uniform magnetic field , with its velocity in a direction perpendicular to . The proton moves in a circular path of radius rp.

(a) In terms of rp, determine the radius rd of the circular orbit for the deuteron.

rd =

(b) In terms of rp, determine the radius r for the alpha particle.
r =

asked Feb 10, 2012 in Physics

Using conservation of energy, establish that that initial potential energy is equal to the final kinetic energy.

initial potential = final kinetic

replace these with the proper equations and we get:

q*V = (1/2)m*v^2  (where q=charge, V=voltage, m=mass, v=velocity)

Solving for v we get that:

v = squareroot(2q*V / m)

Now establish two equations relating magnetic force:

magnetic force = q*v*B = m*v^2 / r  (*where B=magnetic field, r=radius)

solving for r we get:

r = m*v / (q*B)  =  (m / (q*B)) * squareroot(2q*V / m)

simplifying:

r = squareroot((2m*V) / (qB^2))

Therefore,

answered Feb 18, 2012 by ~Expert~ (3,020 points)
edited Mar 8, 2012 by kirby