Two charges, 4 µC and -8 µC, are placed on x-axis at x= -6 m and x=6 m.  Determine the magnitude and direction of the electric field on the y-axis at y = 8 m.

Two point charges are placed on the x axis as shown in (Figure 1). The first charge, q1 = 8.00 nC , is placed a distance 16.0 m from the origin along the positive x axis; the second charge, q2 = 6.00 nC , is placed a distance 9.00 m from the origin along the negative x axis. Find the x-component of the electric field at the origin, point O. Express your answer in newtons per coulomb to three significant figures, keeping in mind that an x component that points to the right is positive. Now, assume that charge q2q2 is negative; q2=−6nCq2=−6nC, as shown in (Figure 2). What is the x-component of the net electric field at the origin, point O? Express your answer in newtons per coulomb to three significant figures, keeping in mind that an x component that points to the right is positive.

A charge q1=+2q is at the origin, and a charge q2=−q is on the x-axis at x=a, where a>0. Find the expression Ex<0 for the total electric field on the x-axis in the region x<0. Use k to represent Coulomb's constant.   Find the expression E0<x<a for the total electric field on the x-axis in the region 0<?<?.   Find the expression Ea<x for the total electric field on the x-axis in the region ?<?.   Determine all the points x on the x-axis where the electric field is zero. If there is more than one point, enter them as a comma‑separated list.

Four point charges of equal magnitude Q = 45 nC are placed on the corners of a rectangle of sides D1 = 16 cm and D2 = 9 cm. The charges on the left side of the rectangle are positive while the charges on the right side of the rectangle are negative. Use a coordinate system where the positive y direction is up and the positive x direction is to the right. a) Calculate the horizontal component of the net force, in newtons, on the charge which lies at the lower left corner of the rectangle.  b) Calculate the vertical component of the net force, in newtons, on the charge which lies at the lower left corner of the rectangle.  c)Calculate the magnitude of the net force, in newtons, on the charge located at the lower left corner of the rectangle.  d) Calculate the angle of the net force vector relative to the +x axis, with the positive direction being counterclockwise from the positive horizontal axis. Enter an angle between -180° and 180°.