Question

How many turns per linear meter should have a solenoid so that when placed around a vacuum cathode ray tube can maintain a 100eV electron circulating in the tube axis in a circle of 1cm radius. The solenoid carries a current of 1 A.

Ans: Aprox, 2700 turns/meter

Answer 1

Speed of the electron ..1

Here M=9.11*10^-31 kg , 100eV=100*1.6*10^-19 =16*10^-18 J

Put these value in equation 1

9.11*10^-31V² =2*16*10^-18

V² =320*10^-19/9.11*10^-31

V²=35.13*10¹²

V=5.927*10⁶ m/s

now magnetic force on the electron

=qVB=MV²/R

B=MV/Rq ..2

for solenoid ..3

From equation 1 and 3

N=MV/IRq

4*10^-7 , R=1cm=0.01 m ,I=1.0A q=1.6*10^-19C

N=9.11*10^-31*5.927*10⁶/4*10^-7*1*0.01*1.6*10^-19

N=2.686*10³

N=~2700 turns