Four point charges are placed at the four corners of a square. Each side of the square has a length L. Find the magnitude of the electric force onq2 due to all three charges q1, q3 and q4 for
L = 1 m and all q = 1.55 �C.
Answer in units of N
To find the magnitude of the electric force on q2 due to q1, q3, and q4, we can use the principle of superposition. The electric force exerted by each charge on q2 can be calculated individually using Coulomb's law, and then the forces can be added together to find the net force.
Coulomb's law states that the electric force F between two charges q1 and q2 separated by a distance r is given by:
F = k * (q1 * q2) / r^2
Where k is the electrostatic constant, which has a value of 8.99 × 10^9 Nm^2/C^2.
In this case, we have four charges at the corners of a square. Let's label the charges as follows:
q1 is the charge at the top left corner,
q2 is the charge at the top right corner,
q3 is the charge at the bottom right corner,
q4 is the charge at the bottom left corner.
We want to find the magnitude of the electric force on q2, so we need to calculate the forces due to q1, q3, and q4 individually, and then add them together.
The distance between q1 and q2 is the length of the side of the square, L.
The distance between q3 and q2 is also L, as they are on adjacent sides of the square.
The distance between q4 and q2 is √2L, as they are on opposite sides of the square.
Using Coulomb's law, we can calculate the electric force on q2 due to each charge:
Force due to q1 on q2: F1 = (8.99 × 10^9 Nm^2/C^2) * ((1.55 × 10^-6 C) * (1.55 × 10^-6 C)) / L^2
Force due to q3 on q2: F3 = (8.99 × 10^9 Nm^2/C^2) * ((1.55 × 10^-6 C) * (1.55 × 10^-6 C)) / L^2
Force due to q4 on q2: F4 = (8.99 × 10^9 Nm^2/C^2) * ((1.55 × 10^-6 C) * (1.55 × 10^-6 C)) / (2L)^2
Finally, the net force on q2 is the vector sum of these forces:
Net Force on q2 = F1 + F3 + F4
Calculating these values will give you the magnitude of the electric force on q2 due to all three charges q1, q3, and q4.