Please show ALL work with correct units Thank you 19 An ele

.

Please show ALL work with correct units. Thank you.

19. An electron follows a helical path in a uniform magnetic field of magnitude 0.300 T. The pitch of the path is 6.00 m, and the magnitude of the force on the electron is 2.00 x 10 19S N. What is the electron\'s speed? -15

Solution

The magnetic force

B q v = 2.00 * 10^-15

0.300 * 1.60 * 10^-19 * v = 2.00 * 10^-15

v = 41667 m/s

The magnetic force is the centripetal force

m v²/ r = 2.00 * 10^-15

r = m v² / 2.00 * 10^-15

= 9.11 * 10^-31 * 41667² / 2.00 * 10^-15

= 7.91 * 10^-7 m

w = v / r , w = 2 pi / T

T = 2 pi r / v = 2 pi * 7.91 * 10^-7/ 41667 = 1.19 * 10^-10 s

v_x = 6 * 10^-6 / 1.19 * 10^-10

= 50420 m/s

Overall speed = sqrt (41667² + 50420²)

= 6.5 * 10⁴ m/s