Ch 44: Particle Physics and Cosmology

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 44: Particle Physics and Cosmology

문제 10a

44장, 문제 10a

The magnetic field in a cyclotron that accelerates protons is $1.70$ T. How many times per second should the potential across the dees reverse? (This is twice the frequency of the circulating protons.)

검증된 단계별 안내

Determine the relationship between the cyclotron frequency and the magnetic field. The cyclotron frequency (also called the angular frequency) is given by the formula:

f = \frac{q}{2πm} B

, where

q

is the charge of the proton,

m

is the mass of the proton, and

B

is the magnetic field strength.

Substitute the known values into the formula. The charge of a proton is

q = 1.60 \times 10 ⁻ 19

C, the mass of a proton is

m = 1.67 \times 10 ⁻ 27

kg, and the magnetic field strength is

B = 1.70

Calculate the cyclotron frequency using the formula:

f = \frac{q}{2πm} B

. This will give the frequency of the circulating protons in hertz (Hz).

Since the potential across the dees reverses twice per cycle of the proton's motion, multiply the cyclotron frequency by 2 to find the required frequency of the potential reversal.

Express the final result in hertz (Hz) after performing the calculations, ensuring the units are consistent throughout the process.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Cyclotron Frequency

Cyclotron frequency refers to the frequency at which a charged particle orbits in a magnetic field. It is determined by the charge of the particle, the mass of the particle, and the strength of the magnetic field. For protons in a magnetic field, the frequency can be calculated using the formula f = (qB)/(2πm), where q is the charge, B is the magnetic field strength, and m is the mass of the proton.

Dees in a Cyclotron

In a cyclotron, the 'dees' are the two D-shaped electrodes that create an oscillating electric field to accelerate charged particles. As protons move between the dees, they gain energy from the electric field, which reverses direction at a specific frequency. The frequency of the electric field must match the cyclotron frequency of the protons to ensure efficient acceleration.

Magnetic Field Strength

Magnetic field strength, measured in teslas (T), is a measure of the intensity of the magnetic field. In a cyclotron, a stronger magnetic field allows for higher energy acceleration of particles. The magnetic field influences the radius of the particle's path and its frequency of rotation, which is crucial for determining how often the electric potential across the dees must reverse to maintain synchronization with the protons.