Identical point charges Q are placed at each of the four corners of a 3.0 m * 4.0 m rectangle.If Q = 40 $\mu$C,what is the magnitude of the electrostatic force on any one of the charges?
A)3.0 N
B)2.4 N
C)1.8 N
D)3.7 N
E)2.0 N

Question

Quizplus · Accepted Answer

The electric force between two charges q1 and q2 separated by a distance r is given by Coulomb's law: F = k(q1*q2)/r^2, where k is the Coulomb constant. 
In this case, since all four charges are identical and are placed at the corners of a rectangle, the force on any one charge due to the other three identical charges can be found by considering only the components of the force in the direction towards the other charges. 
The distance between any two adjacent charges is (3^2 + 4^2)^0.5 = 5.0 m. Thus, the magnitude of the force on any one charge due to each of the other three charges is F = k(Q^2)/25. 
There are three such forces acting on any one charge, and they are all at an angle of 45 degrees to the horizontal and vertical axes. Thus, the total force on any one charge is given by:
Ftotal = 2Fcos(45) + F = 2k(Q^2)/50 + k(Q^2)/25 = (3/10)k(Q^2)/25 
Plugging in the values of k and Q and simplifying, we get:
Ftotal = (9*10^9 N.m^2/C^2)*(40*10^-6 C)^2*(3/10)/(25 m^2) = 2.4 N
Therefore, the answer is choice B.

Identical Point Charges Q Are Placed at Each of the Four