An Electron enters a uniform magnetic field B = 0.23 T at

Chapter 15, Problem 87GP

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QUESTION:

An electron enters a uniform magnetic field \(B=0.23 \mathrm{~T}\) at a \(45^{u}\) angle to \(\vec{B}\). Determine the radius  and pitch  (distance between loops) of the electron's helical path assuming its speed is \(3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\). See Fig. .      

FIGURE 20-72 Problem 87.

Equation Transcription:

     

   

     

Text Transcription:

B=0.23 T    

45u  

\vec B    

3.0 x 106 m/s

Questions & Answers

QUESTION:

An electron enters a uniform magnetic field \(B=0.23 \mathrm{~T}\) at a \(45^{u}\) angle to \(\vec{B}\). Determine the radius  and pitch  (distance between loops) of the electron's helical path assuming its speed is \(3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\). See Fig. .      

FIGURE 20-72 Problem 87.

Equation Transcription:

     

   

     

Text Transcription:

B=0.23 T    

45u  

\vec B    

3.0 x 106 m/s

ANSWER:

Step 1 of 2

Initial velocity is:

Magnetic field is:

Initial angle:

The component of the velocity along the magnetic field is .

The electron travels in a circular path with the velocity  perpendicular to the field.

The centripetal force is equal to the magnetic force on it.

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