Question

Charge q₁ = -6.5 nC is located at the coordinate system origin, while charge q₂ = 3.5 nC is located at (a, 0), where a = 1.2 m. The point P has coordinates (a, b), where b = 3.4 m.

a)At the point P, find the x-component of the electric field E_x in units of N/C.

b)At the point P, find the y-component of the electric field E_y in units of N/C.

Answer 1

here,

q1 = - 6.5 nC = - 6.5 * 10^-9 C is at (x1 , y1) = (0,0)

q2 = 3.5 nC = 3.5 * 10^-9 C is at (x2 , y2) = (1.2,0)

point P , (x3 ,y3) = (1.2 m , 3.4 m )

theta = arctan(3.4/1.2) = 70.56 degree

a)

the x-component of the electric field , Ex = - K * q1 /(a^2 + b^2) * cos(theta)

Ex = - 9 * 10^9 * 6.5 * 10^-9 /(1.2^2 + 3.4^2) * cos(70.56) N/C

Ex = - 1.5 N/C

b)

the y-component of the electric field , Ey = - K * q1 /(a^2 + b^2) * sin(theta) + K * q2 /b^2

Ey = - 9 * 10^9 * 6.5 * 10^-9 /(1.2^2 + 3.4^2) * sin(70.56) + 9 * 10^9 * 3.5 * 10^-9 /3.4^2 N/C

Ey = - 1.51 N/C