A proton circulates in a cyclotron, beginning approximately at restat the center

Question

A proton circulates in a cyclotron, beginning approximately at restat the center. Whenever it passes through the gap between dees, theelectric potential difference between the dees is 190 V. (a) By how much does its kinetic energy increase with each passagethrough the gap?
eV

(b) What is its kinetic energy as it completes 500 passes through the gap?
keV

(c) Let r500 be the radius of its circular path inthe dee that it enters as it completes those 500 passes, andlet r501 beits next radius, as it enters a dee the next time. By whatpercentage does the radius increase when it changesfrom r500 to r501? (r501 - r500) / r500%)
%
(a) By how much does its kinetic energy increase with each passagethrough the gap?
eV

(b) What is its kinetic energy as it completes 500 passes through the gap?
keV

(c) Let r500 be the radius of its circular path inthe dee that it enters as it completes those 500 passes, andlet r501 beits next radius, as it enters a dee the next time. By whatpercentage does the radius increase when it changesfrom r500 to r501? (r501 - r500) / r500%)
%

Explanation / Answer

V = 190 V, a) kinetic energy K1 = eV = 190 eV b) K500 = 500K = 95 keV c) for radius r, qvB = mv2/r so r = mv/(qB) = [2m(mv5002/2)]/(qB) =(2mK500)/(qB) for r500 = (2mK500)/(qB), for r501 = (2mK501)/(qB), (r501 - r500)/r500 =r501/r500 - 1 =(K501/K500) - 1 but K501 = K500 + K1 = 95.19keV (r501 - r500)/r500 =0.09995%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.