Question

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

Answer 1

The electron would need to attain a speed of at least $2.813*10^7 m/s$

Data;

• diameter of sphere = 2.0mm
• charge = 1.0 nC

The distance of the electron from the center of the sphere  = (1 + 1)mm = 2mm.

$2mm = 2.0*10^-3m$

Centrifugal Force and Coulomb's law

Using centrifugal force of attraction and coulomb's law, we can determine the speed which the electron needs.

$\frac{mV^2}{R}=\frac{Kq_1q_2}{r^2}\\ K = \frac{1}{4\pi \epsilon } \\ V^2 = \frac{q_1R\\}{4\pi \epsilon \ m r} \\v = \sqrt{\frac{1.0*10^-^9*1.602*10^-^1^9}{4\pi \epsilon *9.1*10^-^3^1*2.0*10^_3} }$

Solving the above, we would have

$v = 2.813*10^7m/s$

The electron would need to attain a speed of at least 2.813*10^7 m/s

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