The four cases below all show a ball with a charge of -3q at the top right corne

Question

The four cases below all show a ball with a charge of -3q at the top right corner of a square. Then there is either one, two, or three additional charged balls, each ball located at a different corner of the square. For the rest of the problem, use q = 4.50 Times 10^-6 C, and L = 30.0 cm, as well as k = 8.99 Times 10^9 N m^2/C^2. In Case C, calculate the magnitude of the net electric field at the center of the square. N/C In Case A, calculate the magnitude of the net electric field at the bottom left corner of the square. N/C

Explanation / Answer

the electric field due to the two +q charges get cancels out

the only filed is due to -3q

E = k*3q/r^2

r = (1/2)*sqrt(L^2+L^2) = L/sqrt2

E = (8.99*10^9*3*4.5*10^-6*2)/(0.3^2)

E = 2697000 N/C

++++++++++

(c)

q1 = +q

q2 = -3q

E1y = -k*q1/L^2 = -(8.99*10^9*4.5*10^-6)/(0.3^2) = -449500 N/C

E1x = 0

----------------

E2x = k*q2*cos45/2L^2 = (8.99*10^9*3*4.5*10^-6*cos45)/(2*0.3^2)

E2x = 476766.75 N/C

E2y = k*q2*cos45/2L^2 = (8.99*10^9*3*4.5*10^-6*cos45)/(2*0.3^2)

E2y = 476766.75 N/C

Ex = E1x + E2x = 476766.75 N/C

Ey = -449500 + 476766.75 = 27266.75 N/C

E = sqrt(Ex^2 + Ey^2)

E = sqrt(476766.75^2+27266.75^2) = 477545.82 N/C

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