Three equal charges of amount Q, -Q and 2Q, are placed at the vertices of a squa

Question

Three equal charges of amount Q, -Q and 2Q, are placed at the vertices of a square of a side a as illustrated. Determine:
a) The total electric field (both magnitude and direction) produced by the three charges at point A. Make sure to draw eletric field vectors and its components on the figure.
b) The total electric potential produced by the three charges at point A.
c) The Couloumb force at point A (both magnitude and direction) if there is a charge -Q placed at A.
d) Given the value of Q=9.50nC, a is 6.00cm, find numerical values of electric field and force.

Three equal charges of amount Q, -Q and 2Q, are placed at the vertices of a square of a side a as illustrated. Determine: The total electric field (both magnitude and direction) produced by the three charges at point A. Make sure to draw eletric field vectors and its components on the figure. The total electric potential produced by the three charges at point A. The Couloumb force at point A (both magnitude and direction) if there is a charge -Q placed at A. Given the value of Q=9.50nC, a is 6.00cm, find numerical values of electric field and force.

Explanation / Answer

a)

Ex = -k(2Q)/a^2 - kQ/2a^2 = -kQ/a^2 (2 + 1/2) = -2.5 k Q/a^2

Ey = k(Q)/a^2 - kQ/2a^2 = kQ/a^2 (1 - 1/2) = 0.5 k Q/a^2

E = sqrt(Ex^2 + Ey^2) = sqrt((-2.5 k Q/a^2)^2 + (0.5 k Q/a^2)^2) = 6.5 k Q/a^2

direction: 180 - arctan(0.5/2.5) = 169 degrees

b)

V = k (2Q)/a - k Q/a + k Q/(sqrt(2) a) = (kQ/a) (2 - 1 + 1/sqrt(2)) = 1.707 k Q/a

c)

magnitude:

F = Q E = 6.5 k Q^2/a^2

direction:

180 + 169 = 349 degrees

e)

E = 6.5 k Q/a^2 = 6.5*9e9*9.5e-9/(0.06*0.06) = 1.54 x 10^5 N/C

F = 6.5 k Q^2/a^2 = 6.5*9e9*9.5e-9**9.5e-9/(0.06*0.06) = 1.47 x 10^-3 N/C

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