The drawings show three charges that have the same magnitude but different signs. In all cases the distance d between the charges is the same. The magnitude of the charges is |q|= 5.5 µC, and the distance between them is d = 4.3 mm. Determine the magnitude of the net force on charge 2 for each of the three drawings.
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To determine the magnitude of the net force on charge 2 in each of the three drawings, we need to apply Coulomb's Law.
Coulomb's Law states that the magnitude of the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the magnitude of the force
- k is the electrostatic constant (k = 8.99 * 10^9 N m^2/C^2)
- |q1| and |q2| are the magnitudes of the two charges
- r is the distance between the charges
In this case, the charges have the same magnitude, |q| = 5.5 µC, and the distance between them is d = 4.3 mm (which we need to convert to meters).
Step 1: Convert the distance to meters:
d = 4.3 mm = 4.3 * 10^-3 m
Step 2: Calculate the magnitude of the force (net force on charge 2) for each drawing:
Drawing 1:
The net force on charge 2 is the sum of the repulsive force between charge 2 and charge 1 and the attractive force between charge 2 and charge 3.
F1 = k * (|q|^2) / d^2 = (8.99 * 10^9 N m^2/C^2) * (5.5 * 10^-6 C)^2 / (4.3 * 10^-3 m)^2
Drawing 2:
The net force on charge 2 is the sum of the attractive force between charge 2 and charge 1 and the attractive force between charge 2 and charge 3.
F2 = k * (|q|^2) / d^2 = (8.99 * 10^9 N m^2/C^2) * (5.5 * 10^-6 C)^2 / (4.3 * 10^-3 m)^2
Drawing 3:
The net force on charge 2 is the sum of the attractive force between charge 2 and charge 1 and the repulsive force between charge 2 and charge 3.
F3 = k * (|q|^2) / d^2 = (8.99 * 10^9 N m^2/C^2) * (5.5 * 10^-6 C)^2 / (4.3 * 10^-3 m)^2
Step 3: Calculate the magnitude of the net force for each drawing:
The magnitude of the net force is the absolute value of the calculated force F1, F2, F3.
Finally, substitute the values into the respective formulas to calculate the magnitude of the net force on charge 2 for each of the three drawings.