Four identical point charges are located on the corners of rectangle as shown q1 Q2 Q3 and Q4 (g=10 microcoulomb) with dimensions of 60 cm by 15 cm. Calculate the magnitude and direction on Q3 by the other three charges
Q=10 microcoulomb
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www.quora.com/There-are-four-equal-charges-that-are-kept-at-each-corner-of-a-square-How-do-I-calculate-the-force-experienced-by-one-charge-What-is-the-final-expression
Student
To calculate the magnitude and direction of the force on Q3 due to Q1, Q2, and Q4, we can use Coulomb's Law. Coulomb's Law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
1. Start by assigning variables to the given values:
- q1 = Charge on Q1
- q2 = Charge on Q2
- q4 = Charge on Q4
- g = 10 microcoulomb (given)
2. Calculate the distances between Q3 and the other charges:
- Distance between Q3 and Q1 = diagonal length of the rectangle = √((60 cm)^2 + (15 cm)^2)
- Distance between Q3 and Q2 = length of the rectangle = 60 cm
- Distance between Q3 and Q4 = width of the rectangle = 15 cm
3. Apply Coulomb's Law to calculate the force between Q3 and each of the other charges:
Force between Q3 and Q1:
- Calculate the distance between Q3 and Q1 (d1) using the diagonal length of the rectangle.
- Apply Coulomb's Law:
Force (F1) = (k * q1 * g) / (d1^2)
Here, k is Coulomb's constant, approximately equal to 9 x 10^9 N m^2/C^2.
Force between Q3 and Q2:
- Calculate the distance between Q3 and Q2 (d2) using the length of the rectangle.
- Apply Coulomb's Law:
Force (F2) = (k * q2 * g) / (d2^2)
Force between Q3 and Q4:
- Calculate the distance between Q3 and Q4 (d4) using the width of the rectangle.
- Apply Coulomb's Law:
Force (F4) = (k * q4 * g) / (d4^2)
4. Finally, calculate the net force on Q3 by summing up the individual forces in both magnitude and direction. The direction of the net force can be found by considering the vector sum of the individual forces.
Net force on Q3 = F1 + F2 + F4
You can now calculate the magnitudes and directions of the forces on Q3 by substituting the values of q1, q2, q4, k, g, and the distances (d1, d2, and d4) into the formulas outlined above.