Chapter 28: Q23P (page 830)

What uniform magnetic field, applied perpendicular to a beam of electrons moving at $1 .30 \times 10^{6}$ m/s, is required to make the electrons travel in a circular arc of radius 0.350 m?

Short Answer

Expert verified

The required magnetic field is $2.11 \times 10^{- 5} T$ .

Step by step solution

Listing the given quantities

Velocity isV = . $1.3 \times 10^{6} m/s$
Radius is r =. $0.350 m$

Understanding the concept of centripetal force and magnetic field

Weuse the equilibrium condition of the magnetic force on the electron and centripetal force due to the circular path.

Formula:

$F_{m} = q v B$

$F_{c} = \frac{m v^{2}}{r}$

Step 3: Explanation

For the circular motion of an electron:

$\begin{matrix} F_{m} = F_{c} \\ q v B = \frac{m v^{2}}{r} \\ B = \frac{m v}{r q} \end{matrix}$

Substituting the given values in the above expression, and we get,

$\begin{matrix} B = \frac{9.11 \times 10^{- 31} \times 1.3 \times 10^{6}}{0.35 \times 1.6 \times 10^{- 19}} \\ = 2.11 \times 10^{- 5} T \end{matrix}$

The required magnetic field is $2.11 \times 10^{- 5} T$ .

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What uniform magnetic field, applied perpendicular to a beam of electrons moving at $1 .30 \times 10^{6}$ m/s, is required to make the electrons travel in a circular arc of radius 0.350 m?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of centripetal force and magnetic field

Step 3: Explanation

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What uniform magnetic field, applied perpendicular to a beam of electrons moving at 1.30×106 m/s, is required to make the electrons travel in a circular arc of radius 0.350 m?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of centripetal force and magnetic field

Step 3: Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Fundamentals of Physics

Mechanics and Materials

Geometrical and Physical Optics

Measurements

Magnetism

Study anywhere. Anytime. Across all devices.

What uniform magnetic field, applied perpendicular to a beam of electrons moving at $1 .30 \times 10^{6}$ m/s, is required to make the electrons travel in a circular arc of radius 0.350 m?