Exam 16: Electric Charge and Electric Field

Two equally charged tiny spheres of mass $1.0 \mathrm {~g}$ are placed $2.0 \mathrm {~cm}$ apart. When released, they begin to accelerate away from each other at $414 \mathrm {~m} / \mathrm { s } ^ { 2 }$ . What is the magnitude of the charge on each sphere, assuming only that the electric force is present? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Four point charges of equal magnitudes but with varying signs are arranged on three of the corners and at the center of the square of side $d$ as shown in the figure. Which one of the arrows shown represents the net force acting on the center charge?

A point charge $Q = - 12 \mu \mathrm { C }$ , and two other charges $q _ { 2 }$ and $q _ { 2 }$ , are placed on $x - y$ axes as shown in the figure. The electric force components on charge $Q$ are $F _ { x } = + 0.005 \mathrm {~N}$ and $F _ { y } =$ $- 0.003 \mathrm {~N} . \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right)$ (a) How many excess electrons are there in charge $Q$ ? (b) What are the charges $q 1$ and q2, including their signs?

In outer space, a positive charge $q$ is released near a positive fixed charge $Q$ , as shown in the figure. As $q$ moves away from $Q$ , what is true about the motion of $q$ ? (There may be more than one correct choice.)

Two point charges of $+ 5.00 \mu \mathrm { C }$ and $+ 8.00 \mu \mathrm { C }$ are placed inside a cube having sides $0.100 \mathrm {~m}$ long. What is the net electric flux passing through the surface of the cube? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $\mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ ) A) $0.450 \times 10 ^ { 6 } \mathrm { Nm } ^ { 2 } / \mathrm { C }$ B) $1.47 \times 10^6 \mathrm { Nm } ^ { 2 } / \mathrm { C }$ C) $3.80 \times 10^6 \mathrm { Nm } ^ { 2 } / \mathrm { C }$ D) $4.20 \times 10 ^ { 6 } \mathrm { Nm } ^ { 2 } / \mathrm { C }$ E) $0.340 \times 10 ^ { 6 } \mathrm { Nm } ^ { 2 } / \mathrm { C }$

Three point charges are located on the $x$ -axis at the following positions: $Q _ { 1 } = + 2.00 \mu \mathrm { C }$ is at $x =$ $1.00 \mathrm {~m} , Q _ { 2 } = + 3.00 \mu \mathrm { C }$ is at $\mathrm { x } = 0.00$ , and $Q _ { 3 } = - 5.00 \mu \mathrm { C }$ is at $x = - 1.00 \mathrm {~m}$ . What is the magnitude of the electric force on $Q 2 ? \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right.$ )

Two large closely-spaced parallel metal plates are uniformly and oppositely charged and the electric field between them is $7.6 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { C }$ . (a) What is the charge per unit area on each plate? (b) If the plates are now moved two times farther apart, what is the electric field between the plates?

The force of attraction that a $- 40.0 \mu \mathrm { C }$ point charge exerts on $\mathrm { a } + 108 \mu \mathrm { C }$ point charge has magnitude $4.00 \mathrm {~N}$ . How far apart are these two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

If a charge generator builds a negative static charge of $- 7.00 \mu \mathrm { C }$ , how many electrons are transferred to it during this process. $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

Two parallel square metal plates, $8.4 \mathrm {~cm}$ on each side, are $2.5 \mathrm {~mm}$ apart and carry equal but opposite charge uniformly distributed over their facing surfaces. How much excess charge is there on each plate if the electric field between the plates has a magnitude of $2.0$ $\times 10 ^ { 6 } \mathrm {~N} / \mathrm { C } ? \left( k = 1 / 4 \pi \varepsilon n = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

The zirconium nucleus contains 40 protons, and an electron is $1.0 \mathrm {~nm}$ from the nucleus. What is the electric force on the electron due to the nucleus? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $\mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

An electron is projected with an initial velocity $v _ { 0 } = 8.4 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$ along the $y$ -axis, which is the centerline between a pair of charged plates, as shown in the figure. The plates are $1.0 \mathrm {~m}$ long and are separated by $0.10 \mathrm {~m}$ . A uniform electric field of magnitude $E$ in the $+ x$ -direction is present between the plates. If the magnitude of the acceleration of the electron is measured to be $8.9 \times 10 ^ { 15 } \mathrm {~m} / \mathrm { s } ^ { 2 }$ , what is the magnitude of the electric field between the plates? $\left( e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right.$ , $m _ { \text {electron } } = 9.11 \times 10 - 31 \mathrm {~kg}$ )

Two tiny particles having charges of $+ 7.00 \mu \mathrm { C }$ and $- 9.00 \mu \mathrm { C }$ are placed along the $y$ -axis. The $+ 7.00 - \mu \mathrm { C }$ particle is at $y = 0.00 \mathrm {~cm}$ , and the other particle is at $y = 40.00 \mathrm {~cm}$ . Where must a third charged particle be placed along the $y$ -axis so that it does not experience any net electric force due to the other two particles?

Consider a container of $2.0 \mathrm {~g}$ of hydrogen, $\mathrm { H } 2$ (one mole). Suppose you removed all the electrons and moved them to the other side of the earth (Earth's radius is $6380 \mathrm {~km} , k = 1 / 4$ $\pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , \mathrm {~N} _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 }$ molecules $\left. / \mathrm { mol } , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$ (a) How much charge is left behind after you remove the electrons? (b) What electric force do the protons exert on the electrons after they are separated as described?

A small $0.050 - \mathrm { kg }$ insulating sphere carries a charge of $- 60 \mu \mathrm { C }$ and is hanging by a vertical silk thread from a fixed point in the ceiling. An external uniform vertical electric field is now applied. If the applied electric field has a magnitude of $3000 \mathrm {~N} / \mathrm { C }$ and is directed downward, what is the tension in the silk thread? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

How far apart should two protons be if the electrical force of repulsion on each one is equal to its weight on the earth? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right.$ , $m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ )

A thin spherical copper shell of radius $9.5 \mathrm {~cm}$ carries an excess charge of $- 4.2 \mathrm { nC }$ . How many excess electrons are on (a) the outer surface of the shell, and (b) the inner surface? (e $= 1.60 \times 10 ^ { - 19 } \mathrm { C }$ )

$X$ and $Y$ are two initially uncharged metal spheres on insulating stands, and they are in contact with each other. A positively charged rod $R$ is brought close to $X$ as shown in part (a) of the figure. Sphere $Y$ is now moved away from $X$ , as shown in part (b). What are the final charge states of $X$ and $Y$ ?

Two parallel square metal plates that are $1.5 \mathrm {~cm}$ apart and $22 \mathrm {~cm}$ on each side carry equal but opposite charges uniformly spread out over their facing surfaces. How many excess electrons are on the negative surface if the electric field between the plates has a magnitude of $18,000 \mathrm {~N} / \mathrm { C } ? \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right)$