Final answer:
The magnitude of the total force on the third charge at the origin is calculated using Coulomb's law, summing the forces from both charges. Coulomb's law equation F = k * |q1 * q2| / r^2 is used to find the individual forces, which are then added together.
Step-by-step explanation:
The student is asking to calculate the magnitude of the total force exerted by two point charges on a third charge located at the origin according to Coulomb's law. The first charge (2 × 10-9 C) is 2 meters from the origin, and the second charge (3 × 10-9 C) is 4 meters from the origin. The third charge at the origin is 5 × 10-9 C.
To solve this, we utilize Coulomb's law, which states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance separating them. The formula is:
F = k * |q1 * q2| / r2
where F is the force, k is Coulomb's constant (8.988 × 109 Nm2/C2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
After calculating the force from each individual charge on the charge at the origin, we add the two forces as vectors to find the total force on charge 3. This requires acknowledging the direction of the forces, which, if both charges are positive, will be repulsive. However, since the question only asks for the magnitude, we can simply add the scalar values of the forces, assuming the directions have been accounted for.
To find the total force on the third charge at the origin, we sum up the magnitudes of the forces exerted by charge 1 and charge 2 on it:
Ftotal = Ffrom charge 1 + Ffrom charge 2
Each of these is calculated by substituting the values of the charges and distances into Coulomb's law.