Answer:
r = 0.11 m 
Explanation:
The radius of the proton's resulting orbit can be calculated equaling the force centripetal (Fc) with the Lorentz force ( ), as follows:
), as follows: 
 (1)
  (1)
<u>Where:</u>
<em>m: is the proton's mass =  1.67*10⁻²⁷ kg</em>
<em>v: is the proton's velocity</em>
<em>r: is the radius of the proton's orbit</em>
<em>q: is the proton charge = 1.6*10⁻¹⁹ C</em>
<em>B: is the magnetic field = 0.040 T </em>
Solving equation (1) for r, we have:
 (2)
   (2)
By conservation of energy, we can find the velocity of the proton:
 (3)
   (3)
<u>Where:</u>
<em>K: is kinetic energy</em>
<em>U: is electrostatic potential energy</em>
<em>ΔV: is the potential difference = 1.0 kV </em>
Solving equation (3) for v, we have:
 
   
Now, by introducing v into equation (2), we can find the radius of the proton's resulting orbit:
 
 
Therefore, the radius of the proton's resulting orbit is 0.11 m.
I hope it helps you!