At each corner of a square of side script i there are point charges of magnitude Q, nQ, mQ, and 4Q, where n = 3 and m = 3. Determine the force on the charge mQ due to the other three charges. (mQ is on the bottom right corner, nQ is on the top right corner, Q is on the top left corner, and 4Q is on the bottom left corner)
To determine the force on the charge mQ due to the other three charges, we can 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 them.
Step 1: Calculate the force between mQ and Q:
Since the charge mQ is at the bottom right corner and charge Q is at the top left corner, they are diagonal from each other. The distance between them is the length of the square's side, which is represented as "i". Thus, the distance between them is √(i^2 + i^2) = √2i.
Using Coulomb's Law, the force between mQ and Q can be calculated as:
Force_mQ_Q = (k * mQ * Q) / (distance^2),
where k is the electrostatic constant (k ≈ 9 × 10^9 N m^2/C^2) and distance is √2i.
Step 2: Calculate the force between mQ and nQ:
Since the charge mQ is at the bottom right corner and charge nQ is at the top right corner, they are adjacent to each other. The distance between them is the length of the square's side, which is represented as "i". Thus, the distance between them is "i".
Using Coulomb's Law, the force between mQ and nQ can be calculated as:
Force_mQ_nQ = (k * mQ * nQ) / (distance^2),
where k is the electrostatic constant and distance is i.
Step 3: Calculate the force between mQ and 4Q:
Since the charge mQ is at the bottom right corner and charge 4Q is at the bottom left corner, they are adjacent to each other. The distance between them is the length of the square's side, which is represented as "i". Thus, the distance between them is "i".
Using Coulomb's Law, the force between mQ and 4Q can be calculated as:
Force_mQ_4Q = (k * mQ * 4Q) / (distance^2),
where k is the electrostatic constant and distance is i.
Finally, to determine the net force on mQ due to the other three charges, you need to find the vector sum of the forces:
Net Force = Force_mQ_Q + Force_mQ_nQ + Force_mQ_4Q.
After plugging in the values for Q, nQ, mQ, i, and performing the calculations using Coulomb's Law as explained above, you can determine the force on the charge mQ due to the other three charges.