Chapter 23: Q. 58 (page 656)

A $2.0 - m m$ -diameter glass sphere has a charge of $+ 1.0 n C$ . What speed does an electron need to orbit the sphere $1.0 m m$ above the surface?

Short Answer

Expert verified

The electron needs to orbit the sphere at a speed of $3.97 x 10^{7} m / s$

Step by step solution

Given information and formula

Given :

Diameter of glass sphere : $2.0 - m m$

Charge on glass sphere : $+ 1.0 n C$

Distance of the sphere from the surface : $1.0 m m$

Theory used :

Electrostatic force on a sphere concentric on the center generates the electron centripetal force. That is :

$F_{e} = F_{c}$

Calculating the orbital speed

Electrostatic force on a sphere concentric on the center generates the electron centripetal force.

$F_{e} = F_{c} \Rightarrow \frac{1}{4 π ε_{0}} \times \frac{Q_{e}}{r^{2}} = \frac{m v ²}{r} \Rightarrow \frac{9 \times 10^{9} \times 10^{- 9} \times 1.6 \times 10^{- 19}}{10^{- 3}} = 9.11 \times 10^{- 31} v ² \Rightarrow v^{2} = \frac{1.44 x 10^{- 15}}{9.11 x 10^{- 31}} \Rightarrow v = \sqrt{1.15068 x 10^{- 47}} = 3.97 x 10^{7} m / s$

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A $2.0 - m m$ -diameter glass sphere has a charge of $+ 1.0 n C$ . What speed does an electron need to orbit the sphere $1.0 m m$ above the surface?

Short Answer

Step by step solution

Given information and formula

Calculating the orbital speed

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A 2.0-mm-diameter glass sphere has a charge of +1.0nC. What speed does an electron need to orbit the sphere 1.0mm above the surface?

Short Answer

Step by step solution

Given information and formula

Calculating the orbital speed

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Electricity and Magnetism

Magnetism and Electromagnetic Induction

Linear Momentum

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Study anywhere. Anytime. Across all devices.

A $2.0 - m m$ -diameter glass sphere has a charge of $+ 1.0 n C$ . What speed does an electron need to orbit the sphere $1.0 m m$ above the surface?