1) A particle with mass 1.65×10 12 kg and electric charge 8.22×10 8 C moves perp

Question

1) A particle with mass 1.65×1012 kg and electric charge 8.22×108 C moves perpendicularly to a uniform magnetic field of strength 5.45×103 T. The angular momentum of the particle about the center of its circular orbit is 3.20×1010 kg·m2/s. (a) What is the radius of the circular orbit? (b) What is the speed of the particle?

2) An alpha particle (two protons and two neutrons, with a mass of 6.68×10–27 kg) moves in a circle inside a solenoid. The plane of the circle is perpendicular to the central axis of the solenoid, approximately parallel to the loops, and its radius is 5.00 cm. The speed of the particle is 2250 m/s. (a) What is the strength of the magnetic field inside the solenoid? (b) The solenoid carries a current of 10.0 A. How tightly wound is the solenoid, in loops per meter?

3) A spatially uniform magnetic field B changes with time and induces an electric field E in a region of three-dimensional space containing the origin. The electric field is E = k(sin , cos ) N/C at the point (x, y, z), where = arctan(y/x), and k = 5.3. (a) What is the rate of change of the magnetic flux through the circle x 2 + y 2 = 4.0 m2 in the xy plane? Assume that the area normal points in the positive z direction. (b) Assuming that the flux is zero at time t = 0 s, what is the flux through the circle when t = 10 s? (c) What is the magnetic field strength at t = 10 s?

Explanation / Answer

mass of particle , m = 1.65 *10^-12 kg

electric charge , q = -8.22 *10^-8 C

B = 5.45 *10^-3 T

angular momentum , L = 3.2 *10^-10 Kg.m/s

let v be the speed of particle and r is the radius of orbit

angular momentum , L = m*v*r

3.2 *10^-10 = 1.65 *10^-12 * m*v

r*v = 193.9 -----(1)

now, for the radius of particle ,

r = m*v/(B*q)

r = 1.65 *10^-12 * v/(5.45 *10^-3 * 8.22 *10^-8) ----(2)

solving 1 and 2 ,

r = 0.845 m

v = 229.45 m/s

a) the radius of circular path is 0.845 m

b)

the speed of particle is 229.45 m/s

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