BR Physics II E&M Psg 4, Q32

[futbolboy]

Which of the following statements would NOT be true, if the voltage amplitude across the gap were doubled?

A. An ion would spiral out in less time and be ejected sooner.
B. An ion would be emitted with a greater kinetic energy.
C. The cyclotron frequency would remain unchanged.
D. The magnetic field would remain unchanged.

The answer is B. However, I thought A and B are similar because if the ion is ejected in less time, it must be traveling faster. If it has a greater speed, it must have a greater kinetic energy.

Can someone explain this problem?

---

Members don't see this ad.

 

[Pamplemousse123]

Which of the following statements would NOT be true, if the voltage amplitude across the gap were doubled?

A. An ion would spiral out in less time and be ejected sooner.
B. An ion would be emitted with a greater kinetic energy.
C. The cyclotron frequency would remain unchanged.
D. The magnetic field would remain unchanged.

The answer is B. However, I thought A and B are similar because if the ion is ejected in less time, it must be traveling faster. If it has a greater speed, it must have a greater kinetic energy.

Can someone explain this problem?

I agree. Does anyone know what's going on with B? The answer explanation is somewhat contradictory: it says at one point that choice A is true because each time the ion passes gap, it gains twice the energy. Choice B is false because KE of the ion stays constant. Please help!

 

[BerkReviewTeach]

Which of the following statements would NOT be true, if the voltage amplitude across the gap were doubled?

A. An ion would spiral out in less time and be ejected sooner.
B. An ion would be emitted with a greater kinetic energy.
C. The cyclotron frequency would remain unchanged.
D. The magnetic field would remain unchanged.

The answer is B. However, I thought A and B are similar because if the ion is ejected in less time, it must be traveling faster. If it has a greater speed, it must have a greater kinetic energy.

Can someone explain this problem?

The problem in your reasoning is that less time to eject does not necessarily correlate to greater speed at ejection, but rather a shorter distance traveled before exitting (it takes bigger laps and escapes sooner). It accelerates faster, so it reaches its exit speed sooner, but the exit speed is a fixed value.

The best way to see this is to simplify what a cyclotron is doing. There are two parts. The electric field speeds the particle up as it travels across the gap. Once it leaves the E field, it enters a perpendicular B field, which causes it to turn without speeding up. The B field turns it 180 degrees, so it travels across the gap again (only this time in the opposite direction, so the E field across the gap must be reversed). As it travels across the gap again, it speeds up some more. Again, it leaves the E field and enters a perpendicular B field, which turns it around by 180 degress so it can do the same thing all over again.

So basically, the E field speeds it up and the B field turns it around so it can cross the E field again.

So if the E field is strong, it will speed up even more, entering the B field faster. This causes the ion to take a bigger semicircle in the B field. By taking a bigger semicircle, it completes fewer cycles before the radius is so large that it gets ejected. So it leaves the cyclotron having done less cycles, which means it has left sooner (in less time). However, the speed it has when leaving is unaffected. With a stronger E field, it speeds up more each time it crosses the gap, but it crosses the gap fewer times total before being ejected. The two effects (greater acceleration and fewer total laps) cancel each other out. So the only way to know the speed at ejection is to consider the B force. We know that r = mv/qB, and the particle has a constant m/q ratio and the B field strength is constant, so the r is directly proportional to v. If the ion gets spit out at the same point each time (which would mean it was ejected at the same r), then it must be ejected from the cyclotron at the same speed each time. No matter what, the particle is ejected with the same spped, and therefore the same KE. That makes choice B the statement that is NOT TRUE.

 

[liddojoe]

The problem in your reasoning is that less time to eject does not necessarily correlate to greater speed at ejection, but rather a shorter distance traveled before exitting (it takes bigger laps and escapes sooner). It accelerates faster, so it reaches its exit speed sooner, but the exit speed is a fixed value.

The best way to see this is to simplify what a cyclotron is doing. There are two parts. The electric field speeds the particle up as it travels across the gap. Once it leaves the E field, it enters a perpendicular B field, which causes it to turn without speeding up. The B field turns it 180 degrees, so it travels across the gap again (only this time in the opposite direction, so the E field across the gap must be reversed). As it travels across the gap again, it speeds up some more. Again, it leaves the E field and enters a perpendicular B field, which turns it around by 180 degress so it can do the same thing all over again.

So basically, the E field speeds it up and the B field turns it around so it can cross the E field again.

So if the E field is strong, it will speed up even more, entering the B field faster. This causes the ion to take a bigger semicircle in the B field. By taking a bigger semicircle, it completes fewer cycles before the radius is so large that it gets ejected. So it leaves the cyclotron having done less cycles, which means it has left sooner (in less time). However, the speed it has when leaving is unaffected. With a stronger E field, it speeds up more each time it crosses the gap, but it crosses the gap fewer times total before being ejected. The two effects (greater acceleration and fewer total laps) cancel each other out. So the only way to know the speed at ejection is to consider the B force. We know that r = mv/qB, and the particle has a constant m/q ratio and the B field strength is constant, so the r is directly proportional to v. If the ion gets spit out at the same point each time (which would mean it was ejected at the same r), then it must be ejected from the cyclotron at the same speed each time. No matter what, the particle is ejected with the same spped, and therefore the same KE. That makes choice B the statement that is NOT TRUE.

i seriously just made an account so that i can comment that your explanation was fantastic! thank you so much!