Four charges are located at the four corners of a square of side b:
Q1 = 3 nC at the top right corner,
Q2 = -4 nC at the bottom right corner,
Q3 = 5 nC at the top left corner,
Q4 = 7 nC at the bottom left corner.
What is the electric field at the midpoint between Q3 and Q4?
four point charges field at midpoint
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To find the electric field at the midpoint between Q3 and Q4, follow these steps:
Step 1: Calculate the electric field contribution from each charge at the midpoint.
To find the electric field contribution from each charge, use the expression for electric field due to a point charge:
Electric Field (E) = (k * Q) / r^2
where k is the electrostatic constant (9 x 10^9 N m^2/C^2), Q is the charge magnitude, and r is the distance between the charge and the point of interest.
For Q3 at the top left corner:
E3 = (k * Q3) / r3^2
For Q4 at the bottom left corner:
E4 = (k * Q4) / r4^2
Step 2: Calculate the net electric field at the midpoint.
Since electric field is a vector quantity, we need to sum the electric field contributions from Q3 and Q4 to get the net electric field (E_net):
E_net = E3 + E4
Step 3: Determine the direction of the net electric field.
The direction of the net electric field depends on the vector sum of the individual electric fields. In this case, the electric field contributions from Q3 and Q4 have opposite directions. Thus, the net electric field will have a direction from Q3 to Q4.
Step 4: Calculate the magnitude and finalize the answer.
To determine the magnitude of the net electric field at the midpoint, find the vector sum of the magnitudes of E3 and E4:
|E_net| = |E3 + E4|
Finally, write down the value of the net electric field, including its magnitude and direction at the midpoint between Q3 and Q4.