A $-4.00$-nC point charge is at the origin, and a second $-5.00$-nC point charge is on the $x$-axis at $x = 0.800$ m. Find the net electric force that the two charges would exert on an electron placed at each point in part (a). Note: Part (a) asked to find the electric field (magnitude and direction) at each of the following points on the $x$-axis: (i) $x = 0.200$ m; (ii) $x = 1.20$ m; (iii) $x = -0.200$ m.

Two positive point charges $q$ are placed on the $x$-axis, one at $x = a$ and one at $x = -a$. Derive an expression for the electric field at points on the $x$-axis. Use your result to graph the $x$-component of the electric field as a function of $x$, for values of $x$ between $-4a$ and $+4a$.

A point charge $q_1=-4.00$ nC is at the point $x=0.600$ m, $y=0.800$ m, and a second point charge $q_2=+6.00$ nC is at the point $x=0.600$ m, $y=0$. Calculate the magnitude and direction of the net electric field at the origin due to these two point charges.

A point charge is placed at each corner of a square with side length $a$. All charges have magnitude $q$. Two of the charges are positive and two are negative (Fig. E$21.42$). What is the direction of the net electric field at the center of the square due to the four charges, and what is its magnitude in terms of $q$ and $a$?

A $-4.00$-nC point charge is at the origin, and a second $-5.00$-nC point charge is on the $x$-axis at $x=0.800$ m. Find the electric field (magnitude and direction) at each of the following points on the $x$-axis: (i) $x=0.200$ m; (ii) $x=1.20$ m; (iii) $x=-0.200$ m.

A charge of $-6.50$ nC is spread uniformly over the surface of one face of a nonconducting disk of radius $1.25$ cm. Why is the field in part (a) stronger than the field in part (b)? Why is the field in part (c) the strongest of the three fields? Note: Part (a) asked to find the magnitude and direction of the electric field this disk produces at a point $P$ on the axis of the disk a distance of $2.00$ cm from its center. Part (b) asked to find the magnitude and direction of the electric field at point $P$, supposing that the charge were all pushed away from the center and distributed uniformly on the outer rim of the disk. Part (c) asked to find the magnitude and direction of the electric field at point $P$ if the charge is all brought to the center of the disk.

Two positive point charges $q$ are placed on the $x$-axis, one at $x=a$ and one at $x=-a$. Find the magnitude and direction of the electric field at $x=0$.