Answer to Question 7

In a demonstration electrons are accelerated by a voltage of 1200 V into a uniform magnetic field that is generated by two Helmholtz coils of 500 turns and radius 7.5 cm (and 7.5 cm apart). The radius of the electron path is measured at 3.4 cm. (a) Show that the speed of the electrons is about 2 × 10^{7} m s^{1}; (b) Calculate the magnetic flux density of the field; (c) Calculate the current in the Helmholtz coils.
Mass of an electron = 9.11 × 10^{31} kg; Charge on an electron = 1.6 × 10^{19} C m_{0} = 4p × 10^{7} H m^{1} 
(a) Formula:
v^{2} = (2 × 1.6 × 10^{19} C × 1200 V) ÷ (9.11 × 10^{31} kg) = 4.22 × 10^{14} m^{2} s^{2}
v = 2.1 × 10^{7} m s^{1}
(b) Formula:
B = (9.11 × 10^{31} kg × 2.053 × 10^{7} m s^{1}) ÷ (0.034 m × 1.6 × 10^{19} C) = 3.438 × 10^{3} T = 3.4 × 10^{3} T
(c) Formula:
I = (0.075 m × 3.438 × 10^{3} T) ÷ [(0.8)^{1.5} × 4p × 10^{7} H m^{1 }× 500]
I = 0.57 A
