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Chapter 23: Q. 58 (page 656)

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

Expert verified

The electron needs to orbit the sphere at a speed of 3.97x107m/s

Step by step solution

01

Given information and formula 

Given :

Diameter of glass sphere : 2.0-mm

Charge on glass sphere : +1.0nC

Distance of the sphere from the surface :1.0mm

Theory used :

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

Fe=Fc

02

Calculating the orbital speed

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

Fe=Fc⇒14πε0×Qer2=mv²r⇒9×109×10-9×1.6×10-1910-3=9.11×10-31v²⇒v2=1.44x10-159.11x10-31⇒v=1.15068x10-47=3.97x107m/s

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