Chapter 6: Q13E (page 1520)

(a) What is the speed of a proton that has total energy $1000 G e V$ ? (b) What is the angular frequency v of a proton with the speed calculated in part (a) in a magnetic field of $4.00 T$ ? Use both the nonrelativistic and the correct relativistic expression, and compare the results.

Short Answer

Expert verified

The speed of a proton is $v = 0.99999956 c$ and angular frequency in case of nonrelativistic is $ω_{n r} = 3.83 \times 10^{8} r a d / s$ and in case of relativistic is $ω_{r} = 3.59 \times 10^{5} r a d / s .$

Step by step solution

Definition of Speed

The term speed may be defined as the ratio of distance and time

Determine the speed of a proton is and angular frequency in case of nonrelativistic and in case of relativistic

The relativistic total energy of a particle is $E = γ m c^{2}$

$1000 G e V = γ (0.938 G e V) γ = 1000 G e V / 0.938 G e V γ = 1066$

and the speed of the proton is

1 / \sqrt (1 - v^{2} / c^{2}) = 1066 v^{2} = 1 - 8.798 \times 10^{(} - 7) v^{2} = 0.999999 c^{2} v = 0.99999956 c

Hence, the speed of a proton is $v = 0.99999956 c$

Now the relation between angular frequency and magnetic field is

$ω = | q | B / m$

For nonrelativistic angular frequency

$ω_{n r} = (1.60 \times 10^{(} - 19) C) (4 T) / (1.67 \times 10^{(} - 27) K g) ω_{n r} = 3.83 \times 10^{8} r a d / s$

For relativistic angular frequency

$ω_{r} = (3.83 \times 10^{8} r a d / s) / 1066 ω_{r} = 3.59 \times 10^{5} r a d / s$

Hence, angular frequency in case of nonrelativistic is $ω_{n r} = 3.83 \times 10^{8} r a d / s$ and in case of relativistic is $ω_{r} = 3.59 \times 10^{5} r a d / s .$ .

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(a) What is the speed of a proton that has total energy $1000 G e V$ ? (b) What is the angular frequency v of a proton with the speed calculated in part (a) in a magnetic field of $4.00 T$ ? Use both the nonrelativistic and the correct relativistic expression, and compare the results.

Short Answer

Step by step solution

Definition of Speed

Determine the speed of a proton is and angular frequency in case of nonrelativistic and in case of relativistic

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(a) What is the speed of a proton that has total energy1000GeV ? (b) What is the angular frequency v of a proton with the speed calculated in part (a) in a magnetic field of4.00T ? Use both the nonrelativistic and the correct relativistic expression, and compare the results.

Short Answer

Step by step solution

Definition of Speed

Determine the speed of a proton is and angular frequency in case of nonrelativistic and in case of relativistic

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Modern Physics

Electromagnetism

Conservation of Energy and Momentum

Thermodynamics

Magnetism and Electromagnetic Induction

Study anywhere. Anytime. Across all devices.

(a) What is the speed of a proton that has total energy $1000 G e V$ ? (b) What is the angular frequency v of a proton with the speed calculated in part (a) in a magnetic field of $4.00 T$ ? Use both the nonrelativistic and the correct relativistic expression, and compare the results.