Question

A proton moves in a helical path at speed $v=4.0$ $\times 10^{7} \mathrm{~m} / \mathrm{s}$ high above the atmosphere, where Earth's magnetic field has magnitude $B=1.0 \times 10^{-6} \mathrm{~T}$. The proton's velocity makes an angle of $25^{\circ}$ with the magnetic field. (a) Find the radius of the helix. [Hint: Use the perpendicular component of the velocity.] (b) Find the pitch of the helix-the distance between adjacent "coils." [Hint: Find the time for one revolution; then find how far the proton moves along a field line during that time interval.]

          A proton moves in a helical path at speed $v=4.0$ $\times 10^{7} \mathrm{~m} / \mathrm{s}$ high above the atmosphere, where Earth's magnetic field has magnitude $B=1.0 \times 10^{-6} \mathrm{~T}$. The proton's velocity makes an angle of $25^{\circ}$ with the magnetic field. (a) Find the radius of the helix. [Hint:
Use the perpendicular component of the velocity.]
(b) Find the pitch of the helix-the distance between adjacent "coils." [Hint: Find the time for one revolution; then find how far the proton moves along a field line during that time interval.]

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Added by Joshua M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Vishal Gupta

05/20/2022

Step 1

Given: $m = 1.67 \times 10^{-27} \text{ kg}$ $v = 4.0 \times 10^{7} \text{ m/s}$ $\theta = 25^\circ$ $B = 1.0 \times 10^{-6} \text{ T}$ $q = 1.6 \times 10^{-19} \text{ C}$ Plugging in the values: $r = \frac{(1.67 \times 10^{-27})(4.0 \times Show more…

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A proton moves in a helical path at speed $v=4.0$ $\times 10^{7} \mathrm{~m} / \mathrm{s}$ high above the atmosphere, where Earth's magnetic field has magnitude $B=1.0 \times 10^{-6} \mathrm{~T}$. The proton's velocity makes an angle of $25^{\circ}$ with the magnetic field. (a) Find the radius of the helix. [Hint: Use the perpendicular component of the velocity.] (b) Find the pitch of the helix-the distance between adjacent "coils." [Hint: Find the time for one revolution; then find how far the proton moves along a field line during that time interval.]

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