Identical point charges of +3.3 µC are fixed to three of the four corners of a square. What is the magnitude |q| of the negative point charge that must be fixed to the fourth corner, so that the charge at the diagonally opposite corner experiences a net force of zero?
To find the magnitude of the negative point charge, we need to determine the net force experienced by the charge at the diagonally opposite corner.
Let's break down the problem into steps:
Step 1: Calculate the electric forces between the positive charges and the charge at the diagonally opposite corner.
- Each positive charge exerts an electrostatic force on the charge at the diagonally opposite corner.
- The magnitude of the electric force between two point charges can be calculated using Coulomb's law: F = k * (|q1| * |q2|) / r^2
- In this case, since all the charges have the same magnitude (+3.3 µC), we can write the formula for the magnitude of the electric force as: F = k * (3.3 µC)^2 / r^2
Step 2: Sum up the forces.
- Since the positive charges are arranged at the corners of a square, there will be two forces acting on the charge at the diagonally opposite corner.
- The two forces will have equal magnitudes but opposite directions (since they are acting along the same line).
- So, the net force will be the sum of the two forces.
Step 3: Set the net force to zero and solve for the magnitude of the negative point charge.
- If the net force is zero, it means the charge at the diagonally opposite corner is in equilibrium.
- Equilibrium implies that the magnitude of the negative point charge must be such that the forces generated by the positive charges cancel each other out.
Let's perform the calculations to find the value of the magnitude of the negative point charge:
Step 1: Calculate the electric forces between the positive charges and the charge at the diagonally opposite corner.
- Given: |q| (magnitude of each positive charge) = 3.3 µC
- Given: k (Coulomb's constant) = 9 * 10^9 N m^2/C^2 (this is a constant)
Using the formula: F = k * (3.3 µC)^2 / r^2
Step 2: Sum up the forces.
- Since there are two positive charges, the net force will be twice the force calculated in Step 1.
Step 3: Set the net force to zero and solve for the magnitude of the negative point charge.
- If the net force is zero, it means the forces cancel each other out.
- Let |q|n be the magnitude of the negative charge.
Setting the net force for equilibrium to zero, we can write the following equation:
2 * F = k * (3.3 µC)^2 / r^2
Since we want the net force to be zero, we solve for |q|n:
|q|n = √(2 * F * r^2 / k)
Substituting the values into the equation, we can find the magnitude |q|n.