A cosmic-ray proton in interstellar space has an energy of 12.5 MeV and executes a circular orbit having a radius equal to that of Mars' orbit around the Sun (2.28 × 1011 m). What is the magnetic field (in T) in that region of space? Hint: Fc =FB mv2 = gvB this will give you B = r mv = : now think K.E = gr where K.E can be expressed in terms of Momentum (mv) where p qr and K.E is given in the question but you need to convert that into the Joule (1 eV = 1.6 × 10-19 /) and mass of proton is 1.67× 10¬27 Kg Hope you can do this with this hint
A cosmic-ray proton in interstellar space has an energy of 12.5 MeV and executes a circular orbit having a radius equal to that of Mars' orbit around the Sun (2.28 × 1011 m). What is the magnetic field (in T) in that region of space? Hint: Fc =FB mv2 = gvB this will give you B = r mv = : now think K.E = gr where K.E can be expressed in terms of Momentum (mv) where p qr and K.E is given in the question but you need to convert that into the Joule (1 eV = 1.6 × 10-19 /) and mass of proton is 1.67× 10¬27 Kg Hope you can do this with this hint
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![### Cosmic-Ray Proton in Interstellar Space
A cosmic-ray proton in interstellar space has an energy of **12.5 MeV** and executes a circular orbit with a radius equal to that of Mars' orbit around the Sun (**2.28 × 10¹¹ m**). What is the magnetic field (in T) in that region of space?
**Hint:**
\[ F_c = F_B \]
\[
\frac{mv^2}{r} = qvB \quad \text{this will give you} \quad B = \frac{mv}{qr} = \frac{p}{qr}
\]
Now think:
\[
K.E = \frac{1}{2}mv^2
\]
Where K.E can be expressed in terms of Momentum (mv) where \( p \) is momentum, and K.E is given in the question, but you need to convert that into Joules.
\[
(1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J})
\]
Mass of a proton is \( 1.67 \times 10^{-27} \, \text{Kg} \).
Hope you can do this with this hint!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31330aa5-a64b-4d2f-80e6-6ea74abb2a34%2F622bd1c8-2fc5-4cb4-9bb1-c0e8b0322412%2Ffz83cwq_processed.png&w=3840&q=75)
Transcribed Image Text:### Cosmic-Ray Proton in Interstellar Space
A cosmic-ray proton in interstellar space has an energy of **12.5 MeV** and executes a circular orbit with a radius equal to that of Mars' orbit around the Sun (**2.28 × 10¹¹ m**). What is the magnetic field (in T) in that region of space?
**Hint:**
\[ F_c = F_B \]
\[
\frac{mv^2}{r} = qvB \quad \text{this will give you} \quad B = \frac{mv}{qr} = \frac{p}{qr}
\]
Now think:
\[
K.E = \frac{1}{2}mv^2
\]
Where K.E can be expressed in terms of Momentum (mv) where \( p \) is momentum, and K.E is given in the question, but you need to convert that into Joules.
\[
(1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J})
\]
Mass of a proton is \( 1.67 \times 10^{-27} \, \text{Kg} \).
Hope you can do this with this hint!
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