Step-by-step explanation:
To find the magnitude and direction of the net electric field at the center of the rectangle due to all the charges, you can use the principle of superposition. The net electric field at the center is the vector sum of the electric fields due to each individual charge.
Let's break it down step by step:
Step 1: Calculate the electric field due to each charge at the center of the rectangle.
The electric field due to a point charge q at a distance r is given by:
E = k * (q / r^2)
Where:
E is the electric field,
k is Coulomb's constant (approximately 9 x 10^9 N m^2/C^2),
q is the magnitude of the charge, and
r is the distance from the charge to the center of the rectangle.
For q1:
Magnitude of the electric field (E1) at the center = k * (q1 / r1^2)
Direction of E1 is towards the center (opposite to the displacement vector).
For q2:
Magnitude of the electric field (E2) at the center = k * (q2 / r2^2)
Direction of E2 is towards the center (opposite to the displacement vector).
For q3:
Magnitude of the electric field (E3) at the center = k * (q3 / r3^2)
Direction of E3 is towards the center (opposite to the displacement vector).
For q4:
Magnitude of the electric field (E4) at the center = k * (q4 / r4^2)
Direction of E4 is towards the center (opposite to the displacement vector).
Step 2: Add up all the electric field vectors to get the net electric field (E_net).
E_net = E1 + E2 + E3 + E4
Step 3: Find the magnitude and direction of the net electric field (E_net).
The magnitude of E_net is the vector sum of the magnitudes of E1, E2, E3, and E4.
The direction of E_net is the direction of the resultant electric field vector obtained by adding E1, E2, E3, and E4.
Once you have E_net, you can find the direction and magnitude of the net electric field at the center of the rectangle.