The figure below shows four small charged spheres arranged at the corners of a s
ID: 584284 • Letter: T
Question
The figure below shows four small charged spheres arranged at the corners of a square with side d = 25.0 cm. (Let q_1 = +3.00 nC, q_2 = +4.00 nC, q_3 = +1.00 nC, and q_4 = +9.00 nC. Assume q_3 is located at the origin and +x axis is to the right and the +y axis is up along the page. Express your answers in vector form.) What is the electric field at the location of the sphere with charge +1.00 nC? What is the total electric force exerted on the sphere with charge +1.00 nC by the other three spheres?Explanation / Answer
Electric Field is given by,
X component,
r = sqrt(d^2 + d^2)
r = d*sqrt(2)
Ex = - k*q4/d^2 - k*q2/r^2 * cos(45) i^
Ex = - (8.9*9) / 0.25^2 - (8.9*4.0)/ (0.25^2 * 2) * cos(45) i^
Ex = - 1483 i^ N/C
Y component,
Ey = - k*q1/d^2 - k*q2/r^2 * sin(45) j^
Ey = - (8.9*3.0) / 0.25^2 - (8.9*4.0)/ (0.25^2 * 2) * cos(45) j^
Ey = - 226 j^ N/C
Net Electric Field,
E = - 1483 i^ - 226 j^ N/C
Force, F = q* E
F = - 1483 * 10^-9 i^ - 226 * 10^-9 j^ N