Question

A small blue bead of net charge  2.5×10^-7C is held at 1.3m  i +  3m  j , a small red bead of net charge  4×10^-7C is held at −1.3m  i  + 1.5m  j , and a small green bead of net charge  −6×10^-7C is held at 2.1m  i +  −0.5m  j .

What is the  x -component of the net electric field at the origin?

What is the  y-component of the net electric field at the origin?

What is the magnitude of the net electric field at the origin?

Answer 1

Let OA be the vector from O to point A where charge q1 = 2.5 x 10^-7 C is placed.

OA = (1.3 i + 3 j)

|OA| = 3.27 m

similarly, OB = ( -1.3, 1.5) and OC = (2.1, -0.5)

|OB| = 1.985 m and |OC| = 2.160 m

The angle between OA and x axis is:

Between OB and x axis: [clockwise from -x axis]

and between OC and x axis: [clockwise from +x axis]

so, x component of the net electric field at the origin will be:

similarly, y component of the net electric field is:

The magnitude of the net electric field will be:

.