Question

Two identical spheres carry charges of +0.6 coulomb and -0.2 coulomb, respectively. If these spheres touch, the resulting charge on the first sphere will be
1. +0.8 C 2. +0.2 C 3. -0.3 C 4. +0.4 C

Answer 1

Answer:

2. +0.2 C

Explanation:

When the two spheres touch, the total charge will be redistributed such that the two spheres are at same potential:

$V_1 = V_2$

The potential can be rewritten as ratio between the charge on the sphere (Q) and the capacitance of the sphere (C):

$\frac{Q_1}{C_1}=\frac{Q_2}{C_2}$

Since the two spheres are identical, they have same capacitance:

$C_1 =C_2=C$

So we can write

$\frac{Q_1}{C}=\frac{Q_2}{C}$

$Q_1=Q_2$

And since the total charge is

$Q=+0.6 C-0.2 C=+0.4 C$

And this charge will be redistributed equally on the two spheres ($Q_1 = Q_2$), we have

$Q_1 = Q_2 = \frac{Q}{2}=\frac{+0.4 C}{2}=+0.2 C$