Four particles, each carrying a charge of magnitude 4.0 nC, are at the corners of a square that has a side length of 2.0 m. Calculate the potential (relative to zero at infinity) at the center of the square if (a) all four particles are positively charged, (b) three particles are positively charged and one is negatively charged, and (c) two particles are positively charged and two are negatively charged.

(a) If the potential (relative to infinity) is zero at a point, is the electric field necessarily zero at that point?
(b) If the electric field is zero at a point, is the potential (relative to infinity) necessarily zero there?

Sketch some equipotential lines for the electric field line pattern of a electric dipole.

An electron and a proton are held 2 m apart. The midpoint between the electron and the proton sets the origin of a coordinate system, with the x axis pointing toward the proton. (a) A second electron is moved to the origin from infinity. How much work does this take? (b) Keeping the second electron fixed at the origin, a third electron is sent toward the origin with a velocity of 400 m/s from the location (0 m, 10 m). How close does this electron get to the origin?

Points A, B, and C form the vertices of a triangle in a nonuniform electrostatic field. The electrostatic work done on a particle of charge q as the particle travels from A to B is $W _ { \mathrm { AB } }$, and that done on the particle as it travels from A to C is $W _ { \mathrm { AC } } = - W _ { \mathrm { AB } } / 2$. How much electrostatic work is done on the particle as it travels from B to C?

Six particles, each carrying a charge of 2.0 nC, are equally spaced along the equator of a sphere that has a radius of 0.40 m. What is the electrostatic potential (relative to zero at infinity) (a) at the center of the sphere and (b) at either pole of the sphere?

a proton is fired with a speed of $200,000 \mathrm{~m} / \mathrm{s}$ from the midpoint of the capacitor toward the positive plate. a. Show that this is insufficient speed to reach the positive plate. b. What is the proton's speed as it collides with the negative plate?

Point charges q1 = 50μC and q2 = −25 μC are placed 1.0 m apart. What is the force on a third charge q3 = 20μC placed midway between q1 and q2?

Draw a model of the force between two negatively charged particles. Include in your model how the force changes if the charge of the particles change or if the distance between the particles change.

Figure mentioned shows a thin rod with charge $Q$ that has been bent into a semicircle of radius $R$. Find an expression for the electric potential at the center.

A particle moves with a constant speed of $25 \mathrm{~m} / \mathrm{s}$ in a 90-m-radius circle.

$(a)$ What is its angular speed in radians per second about the center of the circle?

A particle moves in a circle of radius $a$ at constant speed $v$. Find the angular speed and the magnitude of the acceleration.

A uniformly charged rod of length L and total charge Q lies along the x axis. (a) Find the components of the electric field at the point P on the y axis a distance d from the origin. (b) What are the approximate values of the field components when d >> L? Explain why you would expect these results.

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(d)$ Which point has the greater angular speed?