Two charges of # 2 C # and # 8 C# are positioned on a line at points # -3 # and # 6 #, respectively. What is the net force on a charge of # -3 C# at # -2 #?

To calculate the net force on the charge of -3 C at -2, we use Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. The net force is the vector sum of the forces due to each charge.

First, we calculate the force due to the 2 C charge at -3:
$F_1 = \frac{k \cdot |q_1 \cdot q|}{r_1^2}$
$F_1 = \frac{(9 \times 10^9 \cdot 2 \cdot 3)}{1}$
$F_1 = 6 \times 10^9 \, N$

Next, we calculate the force due to the 8 C charge at 6:
$F_2 = \frac{k \cdot |q_2 \cdot q|}{r_2^2}$
$F_2 = \frac{(9 \times 10^9 \cdot 8 \cdot 8)}{64}$
$F_2 = 9 \times 10^9 \, N$

Since both charges exert attractive forces on the -3 C charge, we sum the forces:
$F_{\text{net}} = F_1 - F_2$
$F_{\text{net}} = 6 \times 10^9 - 9 \times 10^9$
$F_{\text{net}} = -3 \times 10^9 \, N$

Therefore, the net force on the charge of -3 C at -2 is $-3 \times 10^9$ N.