Question

A 1.00-mm-diameter glass sphere has a charge of + 1.30nC.
What speed does an electron need to orbit the sphere 1.50mm above the surface?

Answer should be in m/s. Thanks:)

Answer 1

Radius of electronsorbit r = heightof electron abovesurface + radius of sphere

= 1.50mm + 1.00 /2 mm

= 2.00 mm

= 2.00* 10^-3 m

Force exerted on theelectron F = (1/4πε₀)* q * e / r²

q = chargeon sphere

F = 9.0 *10⁹ * 1.30 * 10^-9 * 1.6 * 10^-19 /(2.00 * 10^-3)²

= 4.68* 10^-13 N
--------------------------
This force works as centripetal force,hence

F = m* v² / r

v² = F* r / m

    = 4.68* 10^-13 * 2.00 * 10^-3 / 9.1 *10^-31

    = 1.028* 10¹⁵

required velocity ofelectron v = √(10.28* 10¹⁴)

=3.20* 10⁷ m/s