A uniform magnetic field of magnitude 0.167 T is directed along the positive x a

Question

A uniform magnetic field of magnitude 0.167 T is directed along the positive x axis. A positron moving at 4.99E+6 m/s enters the field along a direction that makes an angle of 61.3deg with the x axis (see figure below).

The motion of the particle is expected to be a helix. The mass of a positron is the same as that of an electron: 9.11e-31 kg. The charge is +1.6e-19 C.

a) Calculate the pitch p of the trajectory.


b) Calculate the radius r of the trajectory.

A uniform magnetic field of magnitude 0.167 T is directed along the positive x axis. A positron moving at 4.99E+6 m/s enters the field along a direction that makes an angle of 61.3deg with the x axis (see figure below). The motion of the particle is expected to be a helix. The mass of a positron is the same as that of an electron: 9.11e-31 kg. The charge is +1.6e-19 C. a) Calculate the pitch p of the trajectory. b) Calculate the radius r of the trajectory.

Explanation / Answer

Here ,

v = 4.99 *10^6 m/s

B = 0.167 T

a) Now , time period of motion = 2*pi*m/Be

T = 2*pi*9.1 *10^-31/(e * 0.167)

T = 2.14 *10^-10 s

Now , pitch = t*v*cos(theta)

pitch = 4.99 *10^6 * cos(61.3) * 2.14 *10^-10

pitch = 5.13 *10^-4 m

B)

Now ,

r = mv/Be

r = 9.1 *10^-31 * 4.99 *10^6 * sin(61.3) /(0.167 * e)

r = 1.49 *10^-4 m

the radius of trajectory is   1.49 *10^-4 m

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