Two charges of # -2 C # and # 6 C# are positioned on a line at points # 3 # and # 4 #, respectively. What is the net force on a charge of # -5 C# at # 0 #?

The source of the electrical force is

Since the total of the forces is the net force,

To calculate the net force on a charge at a given point due to multiple charges, we use Coulomb's law. Coulomb's law states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers.

The net force on a charge of -5 C at 0 due to the charges at 3 and 4 can be calculated separately.

The force due to the -2 C charge at 3 on the -5 C charge at 0 is given by:

[F_{1} = \frac{k \cdot |q_{1}| \cdot |q|}{r_{1}^2}]

And the force due to the 6 C charge at 4 on the -5 C charge at 0 is given by:

[F_{2} = \frac{k \cdot |q_{2}| \cdot |q|}{r_{2}^2}]

Then, the net force on the -5 C charge at 0 is the vector sum of (F_{1}) and (F_{2}):

[F_{net} = F_{1} + F_{2}]

where (k) is Coulomb's constant, (q_{1}) and (q_{2}) are the magnitudes of the charges at 3 and 4 respectively, (q) is the magnitude of the charge at 0, and (r_{1}) and (r_{2}) are the distances between the charges.

We calculate (F_{1}) and (F_{2}) using the given values, then sum them up to find (F_{net}).