Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

What radius circular path does an electron travel if it moves at the same speed and in the same magnetic field as the proton in Exercise \({\rm{22}}{\rm{.13}}\)?

The radius of the circular path of the electron is obtained as: \({\rm{4}}{\rm{.36}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 4}}}}{\rm{ m}}\).

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Circular motion of moving charged particle in a magnetic field

In the presence of a magnetic field, a force acts on the moving charged particle. The direction of this force can be obtained using Fleming’s right-hand rule and can be numerically expressed as

\({\rm{F}} = {\rm{q}}\left( {\vec v \times \vec B} \right)\)

where\({\rm{q,}}\;{\rm{v,}}\;{\rm{and B}}\) are given as the amount of charge, the velocity of the charged particle, and the strength of the magnetic field.

Evaluating the radius of the circular path of the electron

To obtain the circular path of the electron.

The equation used is: \({\rm{r = }}\frac{{{\rm{mv}}}}{{{\rm{qB}}}}\).

The value of \({\rm{m}}\) is the mass of the electron.

The value of \({\rm{q}}\) is the charge of the electron.

The value of \({\rm{e}}\) and \({\rm{B}}\) is the strength of the magnetic field obtained in the exercise \({\rm{22}}{\rm{.13}}\), which is \({\rm{0}}{\rm{.98 T}}\).

Now, solve the previous equation for the value of \({\rm{r}}\) which will be the radius of the path.

\(\begin{aligned}{\rm{r}} &= \frac{{{\rm{mv}}}}{{{\rm{eB}}}}\\ &= \frac{{\left( {{\rm{9}}{\rm{.1 \times 1}}{{\rm{0}}^{{\rm{ - 31}}}}\;{\rm{kg}}} \right){\rm{ \times }}\left( {{\rm{7}}{\rm{.5 \times 1}}{{\rm{0}}^{\rm{7}}}{\rm{ m/s}}} \right)}}{{\left( {{\rm{1}}{\rm{.6 \times 1}}{{\rm{0}}^{{\rm{ - 19}}}}\;{\rm{C}}} \right) \times \left( {{\rm{0}}{\rm{.98 T}}} \right)}}\\ &= {\rm{4}}{\rm{.36}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 4}}}}{\rm{ m}}\end{aligned}\)

Therefore, the radius of the circular path of the electron is: \({\rm{4}}{\rm{.36}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 4}}}}{\rm{ m}}\).

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College Physics (Urone)

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Short Answer

What radius circular path does an electron travel if it moves at the same speed and in the same magnetic field as the proton in Exercise \({\rm{22}}{\rm{.13}}\)?

Step by Step Solution

Circular motion of moving charged particle in a magnetic field

Evaluating the radius of the circular path of the electron

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College Physics (Urone)

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Short Answer

What radius circular path does an electron travel if it moves at the same speed and in the same magnetic field as the proton in Exercise \({\rm{22}}{\rm{.13}}\)?

Step by Step Solution

Circular motion of moving charged particle in a magnetic field

Evaluating the radius of the circular path of the electron

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