Final answer:
Using Coulomb's Law, the net force on the +2 µC test charge placed between +6 µC and +4 µC charges can be calculated by finding the force from each charge and then determining the net force and its direction.
Step-by-step explanation:
Electric Forces and Test Charge
A test charge of +2 µC placed halfway between two charges - one being +6 µC and the other +4 µC - requires the use of Coulomb's Law to determine the net force on the test charge. As the charges are separated by 10 cm and the test charge is equidistant from both, we calculate the force exerted by each charge individually and then combine them to find the net force.
For the charge of +6 µC, the force is given by Coulomb's Law: F = k * |q1 * q2| / r^2, where k is Coulomb's constant (8.9875 × 10^9 N m^2 /C^2). Similarly, we calculate the force exerted by the +4 µC charge. Since both charges are positive, both forces will repel the test charge; thus, the test charge will experience a greater force from the larger charge, and we can determine the direction of the net force is away from the +6 µC charge.
Magnitude of the Force
To find the magnitude, we subtract the force due to the +4 µC charge from the force due to the +6 µC charge since they are in opposite directions. The final answer gives the magnitude and direction of the net force on the test charge.