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Chapter 19: Problem 25

The magnetic field in a cyclotron is \(0.360 \mathrm{T}\). The dees have radius \(82.0 \mathrm{cm} .\) What maximum speed can a proton achicve in this cyclotron?

Short Answer

Expert verified
Answer: The maximum speed a proton can achieve in this cyclotron is 5.71 x 10^7 m/s.

Step by step solution

01

Write down the given information and the cyclotron equation

We are given the magnetic field B = 0.360 T and the radius of the dees, r = 82.0 cm. The charge of a proton is q = +1.60 x 10^(-19) C, and its mass is m = 1.67 x 10^(-27) kg. The cyclotron equation relating these quantities is v = qBr/m.
02

Convert the radius of the dees to meters

Since the radius is given in centimeters, we need to convert it to meters by dividing by 100: r = 82.0 cm / 100 = 0.820 m.
03

Calculate the maximum speed using the cyclotron equation

We can now plug in the values for the charge of the proton (q), the magnetic field (B), the radius of the dees (r), and the mass of the proton (m) into the cyclotron equation v = qBr/m to find the maximum speed: v = (1.60 x 10^(-19) C)(0.360 T)(0.820 m) / (1.67 x 10^(-27) kg) v = 5.71 x 10^7 m/s The maximum speed a proton can achieve in this cyclotron is 5.71 x 10^7 m/s.

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Most popular questions from this chapter

A charged particle is accelerated from rest through a potential difference \(\Delta V\). The particle then passes straight through a velocity selector (field magnitudes \(E\) and \(B\) ). Derive an expression for the charge-to-mass ratio \((q / m)\) of the particle in terms of \(\Delta V, E,\) and \(B\)
Prove that the time for one revolution of a charged particle moving perpendicular to a uniform magnetic field is independent of its speed. (This is the principle on which the cyclotron operates.) In doing so, write an expression that gives the period \(T\) (the time for one revolution) in terms of the mass of the particle, the charge of the particle, and the magnetic field strength.

Imagine a long straight wire perpendicular to the page and carrying a current \(I\) into the page. Sketch some \(\overrightarrow{\mathbf{B}}\) field lines with arrowheads to indicate directions.
The conversion between atomic mass units and kilograms is $$1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{kg}$$ After being accelerated through a potential difference of \(5.0 \mathrm{kV},\) a singly charged carbon ion \(\left(^{12} \mathrm{C}^{+}\right)\) moves in a circle of radius \(21 \mathrm{cm}\) in the magnetic ficld of a mass spectrometer. What is the magnitude of the field?
A \(20.0 \mathrm{cm} \times 30.0 \mathrm{cm}\) rectangular loop of wire carries \(1.0 \mathrm{A}\) of current clockwise around the loop. (a) Find the magnetic force on each side of the loop if the magnetic ficld is 2.5 T out of the page. (b) What is the net magnetic force on the loop?
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