Point charges $q _ { 1 } = + 2.00 \mu \textrm{C}$ and $q _ { 2 } = - 2.00 \mu \textrm{C}$ are placed at adjacent corners of a square for which the length of each side is $3.00 \textrm{ cm}$. Point a is at the center of the square, and point b is at the empty corner closest to $q _ { 2 }$. Take the electric potential to be zero at a distance far from both charges.

(a) What is the electric potential at point a due to $q _ { 1 }$ and $q _ { 2 }$?

(b) What is the electric potential at point b?

(c) A point charge $q _ { 3 } = - 5.00 \mu \textrm{C}$ moves from point a to point $b$. How much work is done on $q _ { 3 }$ by the electric forces exerted by $q _ { 1 }$ and $q _ { 2 }$? Is this work positive or negative?

A particle with charge $+4.20 \textrm{ nC}$ is in a uniform electric field E S directed to the left. The charge is released from rest and moves to the left; after it has moved $6.00 \textrm{ cm}$, its kinetic energy is $+2.20 \times 10^{-6} \textrm{ J}$. What are (a) the work done by the electric force, (b) the potential of the starting point with respect to the endpoint, and (c) the magnitude of $\vec{E}?$

A uniform electric field has magnitude E and is directed in the negative $x-$direction. The potential difference between point $a$ (at $x = 0.60 \textrm{ m}$) and point $b$ (at $x = 0.90 \textrm{ m}$) is $240 \textrm{ V}$.

(a) Which point, $a$ or $b$, is at the higher potential?

(b) Calculate the value of $E$.

(c) A negative point charge $q = - 0.200 \mu\textrm{C}$ is moved from $b$ to $a$. Calculate the work done on the point charge by the electric field.

A particle with charge $+4.20 \mathrm{nC}$ is in a uniform electric field $\vec{E}$ directed to the left. The charge is released from rest and moves to the left; after it has moved $6.00 \mathrm{~cm}$, its kinetic energy is $+2.20 \times 10^{-6} \mathrm{~J}$. What are (c) the magnitude of $\vec{E}$ ?

Point charges $q_4=+2.00 \mu \mathrm{C}$ and $q_2=-2.00 \mu \mathrm{C}$ are placed at adjacent corners of a square for which the length of each side is $3.00 \mathrm{~cm}$. Point $a$ is at the center of the square, and point $b$ is at the empty corner closest to $q_2$. Take the electric potential to be zero at a distance far from both charges. (c) A point charge $q_3=-5.00 \mu \mathrm{C}$ moves from point $a$ to point $b$. How much work is done on $q_3$ by the electric forces exerted by $q_1$ and $q_2$ ? Is this work positive or negative?

A very small sphere with positive charge $q = + 8.00 \mu \textrm{C}$ is released from rest at a point $1.50 \textrm{ cm}$ from a very long line of uniform linear charge density $\lambda = + 3.00 \mu \textrm{C/m}$. What is the kinetic energy of the sphere when it is $4.50 \textrm{ cm}$ from the line of charge if the only force on it is the force exerted by the line of charge?

(a) An electron is to be accelerated from $3.00 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s }$ to $8.00 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s }$. Through what potential difference must the electron pass to accomplish this? (b) Through what potential difference must the electron pass if it is to be slowed from $8.00 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s }$ to a halt?

Two point charges $q_1=$ $+2.40 \mathrm{nC}$ and $q_2=-6.50 \mathrm{nC}$ are $0.100 \mathrm{~m}$ apart. Point $A$ is midway between them; point $B$ is $0.080 \mathrm{~m}$ from $q_1$ and $0.060 \mathrm{~m}$ from $q_2$. Take the electric potential to be zero at infinity. Find (a) the potential at point $A$ :

Three-point charges are arranged as we discussed earlier. Find
(a) the magnitude and
(b) the direction of the electric force on the particle at the origin.

Three-point charges lie along a straight line , where $q_1=6.00 \mu \mathrm{C}, q_2=1.50 \mu \mathrm{C}$, and $q_3=-2.00 \mu \mathrm{C}$. The separation distances are $d_1=$ $3.00 \mathrm{~cm}$ and $d_2=2.00 \mathrm{~cm}$. Calculate the magnitude and direction of the net electric force on (a) $q_1$, (b) $q_2$, and (c) $q_3$.

Point charges of $3.00 \mathrm{nC}$ are situated at each of three corners of a square whose side is $0.200 \mathrm{~m}$. What are the magnitude and direction of the resultant force on a point charge of $-1.00 \mu \mathrm{C}$ if it is placed
(a) at the center of the square,
(b) at the vacant corner of the square?

Point charges $q _ { 1 } = 50 \mu \mathrm { C } \text { and } q _ { 2 } = - 25 \mu \mathrm { C }$ are placed 1.0 m apart. What is the force on a third charge $q _ { 3 } = 20 \mu \mathrm { C }$ placed midway between $q _ { 1 } \text { and } q _ { 2 }$?

Three point charges lie along a straight line, where $q_{1}=6.00 \mu \mathrm{C},$ $q_{2}=1.50 \mu \mathrm{C},$ and $q_{3}=-2.00 \mu \mathrm{C}$. The separation distances are $d_{1}=3.00 \mathrm{cm}$ and $d_{2}=2.00 \mathrm{cm}$. Calculate the magnitude and direction of the net electric force on (a) $q_{1},$ (b) $q_{2}$, and (c) $q_{3}$.

A uniform electric field has magnitude $E$ and is directed in the negative $x$-direction. The potential difference between point $a$ (at $x=0.60 \mathrm{~m}$ ) and point $b$ (at $x=0.90 \mathrm{~m}$ ) is $240 \mathrm{~V}$.