I need your help please.. 1) A point charge is placed at each comer of a square

Question

I need your help please..

1) A point charge is placed at each comer of a square with side length a. The charges all have the same magnitude q. Two of the charges are positive and two are negative, as shown in the following figure.

Part A

What is the direction of the net electric field at the center of the square?

  a) leftward direction

b) upward direction

c) rightward direction

d) downward direction

Part   B

What is the magnitude of the net electric field at the center   of the square due to the four charges in terms of q and a ?

Express your answer in terms of the   variables q, a and appropriate constants.

E=

  

  

  a) leftward direction

b) upward direction

c) rightward direction

d) downward direction

  

Part   B

  

What is the magnitude of the net electric field at the center   of the square due to the four charges in terms of q and a ?

  

Express your answer in terms of the   variables q, a and appropriate constants.

  

  

E=

N/CNN/C N/CN/C      

   A point charge is placed at each comer of a square with side length a. The charges all have the same magnitude q. Two of the charges are positive and two are negative, as shown in the following figure. What is the direction of the net electric field at the center of the square? What is the magnitude of the net electric field at the center of the square due to the four charges in terms of q and a ? Express your answer in terms of the variables q, a and appropriate constants.

Explanation / Answer

1)

partA) d) downward

Part B)

E1 = k*q/r^2

here r = sqrt(a^2+a^2)/2 = a*sqrt(2)/2 = a/sqrt(2)

so, E1 = 2*k*q/a^2

here E1 = E2 = E3 = E4


E12 = sqrt(E1^2 + E2^) = sqrt(2)*E1

E34 = sqrt(E3^2 + E4^2) = sqrt(2)*E1

Enet = E12 + E34 = 2*sqrt(2)*E1 = 4*sqrt(2)*k*q/a^2

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