Answer to Question #183063 in Electricity and Magnetism for KyKy

Question

Spheres A, B, and C have charges +8.0 C, +12.0 C, and -5.0 C, respectively. Spheres A and B touched each other and then separated. Sphere A then touched sphere C and then separated. (a) What is the total charge on the three spheres before and after touching each other? (b) What is the final charge on each sphere assuming they are identical? (c) What is the final charge on each sphere assuming that r_A=r_B=2r_C?

Answer 1

a)

$\Sigma q=q_1+q_2+q_3=+15.0~C,$

b)

$q_B'=\frac{q_A+q_B}{2}=+10.0~C,$

$q'_A=q_C'=\frac{\frac{q_A+q_B}{2}+q_C}{2}=+2.5~C,$

c)

$\frac qr=const,$

$q_B''=\frac{q_A+q_B}{2}=+10.0~C,$

$q''_A=\frac{\frac{q_A+q_B}{2}+q_C}{1+2}=+1.7~C,$

$q_C''=\frac{2(\frac{q_A+q_B}{2}+q_C)}{2+1}=+3.3~C.$