Answer:
0.114m
Explanation:
From the general expression for the radius of the proton's resulting orbit, we have
[tex]r=\frac{mv}{qB}[/tex]
where q is is the charge of the proton [tex]1.6*10^{-19}C[/tex]
m is the mass of the proton [tex]1.67*10^{-27}kg[/tex]
B is the magnetic field [tex]0.040T[/tex]
and v i the speed.
to determine the speed, we use the expression
Kinetic Energy=[tex]qV[/tex]
[tex]1/2mv^{2}=qV[/tex]
where V is the voltage value i.e 1.0kv
and v is the speed
Hence, from simple rearrangement we have the speed v to be
[tex]v=\sqrt{\frac{2Vq}{m}} \\[/tex]
if we substitute value, we have
[tex]v=\sqrt{\frac{2*1000*1.6*10^{-19} }{1.67*10^{-27}}} \\[/tex]
carrying out careful arithmetic we arrive at
[tex]v=4.38*10^{5} m/s[/tex].
using the value for the speed in the expression for the radius of the orbit as stated earlier, we have
[tex]r=\frac{1.67*10^{-27}*4.38*10^{5}}{1.6*10^{-19}*0.04} \\[/tex]
[tex]r=0.114m[/tex]
