Initially at rest, a small copper sphere with a mass of 3.00 middot 10-6 kg and
ID: 1517740 • Letter: I
Question
Initially at rest, a small copper sphere with a mass of 3.00 middot 10-6 kg and a charge of 5.00 middot 10-4C is accelerated through a 7000.-V potential difference before entering a magnetic field of magnitude 4.00 T, directed perpendicular to its velocity. What is the radius of curvature of the sphere's motion in the magnetic field? An accelerator produces alphas using an electric potential difference Vo from 1.50 MV to 9.00 MV as shown below: What is the kinetic energy of the alphas as they leave the accelerator if the electric potential difference Vo on the accelerator is 2.50 MV and they initially start from rest? An analyzing magnet supplies a uniform magnetic field which is perpendicular to the path of the alphas. Calculate the magnitude of the magnetic field required to select a 4.00 MeV alpha for a radius of curvature of 45.0 cm.Explanation / Answer
7)
(a)
Charge of an alpha particle, q = 2*e = 2*1.6*10^-19 C = 3.2 * 10^-19 C
Kinetic Energy = q*Vo
Kinetic Energy = 3.2 * 10^-19 * 2.5 * 10^6 J
Kinetic Energy = 8.0 * 10^-13 J
(b)
Calculating Velocity, of 4.0 MeV alpha,
1/2*m*v^2 = 4.0 * 10^6 * 1.6*10^-19 J
1/2*6.64 * 10^-27 * v^2 = 4.0 * 10^6 * 1.6*10^-19
v = 1.39 * 10^7 m/s
Mgnetic Force, F = q*v*B
m*v^2/r = q*v*B
(6.64 * 10^-27*1.39 * 10^7)/0.45 = (3.2*10^-19*B)
B = 0.64 T