58 Week 1: Discrete Charge and the Electrostatic Field
Problem 8.
Q,mΘL LTwo small spheres of massmare suspended from a common point by threads of lengthL. When
each sphere carries a chargeq, each thread makes an angleθwith the vertical as shown.
a) Show that the chargeqis given by:q= 2Lsinθ√
mgtanθ
ke
wherekeis the electrostatic constant.b) Findqifm= 10 grams,L= 50 cm, andθ= 10◦. You may (as usual) useg= 10 m/sec^2.c) What would happen if both chargesqequalled 1 Coulomb instead of the tiny charge you
obtained in your answer to b)?Note that numbers are given in this problem primarily tojust onceforce you to confront what
a reasonable “size” is for macroscopic electric charges in the laboratory. Note well that it is much,
much smaller than a Coulomb!