Exam 16: Electric Charge and Electric Field

A negatively-charged rod is brought close to (but does not touch) two neutral spheres that are in contact with each other but insulated from the ground. If the two spheres are then separated, what kind of charge will be on the spheres?

A metal sphere of radius $2.0 \mathrm {~cm}$ carries an excess charge of $3.0 \mu \mathrm { C }$ . What is the electric field $6.0 \mathrm {~cm}$ from the center of the sphere? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

The figure shows two unequal charges, $+ q$ and $- Q$ . Charge $- Q$ has greater magnitude than charge $+ q$ . Point $\mathrm { X }$ is midway between the charges. In what section of the line will there be a point where the resultant electric field is zero?

Two tiny beads are $25 \mathrm {~cm}$ apart with no other charges or fields present. Bead A carries $10 \mu \mathrm { C }$ of charge and bead B carries $1 \mu \mathrm { C }$ . Which one of the following statements is true about the magnitudes of the electric forces on these beads?

Two uncharged metal spheres, #1 and #2, are mounted on insulating support rods. A third metal sphere, carrying a positive charge, is then placed near #2. Now a copper wire is momentarily connected between $\# 1$ and #2 and then removed. Finally, sphere $\# 3$ is removed. In this final state

How many electrons are necessary to produce $1.0 \mathrm { C }$ of negative charge? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

Two equal and opposite charges are a small distance apart, forming an electric dipole. A positive charge $+ q$ is placed above these charges, as shown in the figure, equidistant from both of them. Which diagram below best gives the direction of the net force the dipole exerts on the charge $+ q$ ? $+ q$

Four point charges of varying magnitude and sign are arranged on the corners of the square of side $d$ as shown in the figure. Which one of the arrows shown represents the net force acting on the point charge with a charge $+ Q$ ?

A proton is placed in an electric field of intensity $800 \mathrm {~N} / \mathrm { C }$ . What are the magnitude and direction of the acceleration of the proton due to this field? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , \mathrm { m } _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

One point charge $+ Q$ is placed at the center of a square, and a second point charge $- Q$ is placed at the upper-left corner of the square. It is observed that an electrostatic force of magnitude $2.0 \mathrm {~N}$ acts on the positive charge at the center. Now a third charge $- Q$ is placed at the lower-left corner of the square, as shown in the figure. What is the magnitude of the net force that acts on the center charge now?

Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude $F$ due to the other. With time, charge gradually diminishes on both spheres by leaking off. When each of the spheres has lost half its initial charge, what will be the magnitude of the electrostatic force on each one?

A spherical conductor of radius $2.0 \mathrm {~mm}$ carries a charge of $7.1 \mathrm { nC }$ . What is the magnitude of the electrical field at $6.0 \mathrm {~mm}$ from the center of the sphere? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

As shown in the figure, three charges are at corners of a rectangle. The charge in the bottom right corner is $Q = - 90 \mathrm { nC }$ , and all the other quantities are accurate to two significant figures. What is the magnitude of the net electrical force on $Q$ due to the other two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \right.$ $\mathrm { N } \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

What is the charge on $1.0 \mathrm {~kg}$ of protons? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

The electric field at point $P$ due to a point charge $Q$ a distance $R$ away from $P$ has magnitude $E$ . In order to double the magnitude of the field at $P$ , you could

A particle of charge $+ 2 q$ is placed at the origin and particle of charge $- q$ is placed on the $x$ -axis at $x$ $= 2 \mathrm { a }$ . Where on the $x$ -axis can a third positive charge be placed so that the net electric force on it is zero?

A small styrofoam ball of mass $0.120 \mathrm {~g}$ is placed in an electric field of $6000 \mathrm {~N} / \mathrm { C }$ pointing downward. What excess charge must be placed on the ball for it to remain suspended in the field?

As shown in the figure, three charges are at the vertices of an equilateral triangle. The charge $Q$ is $6.7 \mathrm { nC }$ , and all the other quantities are accurate to two significant figures. What is the magnitude of the net electric force on the charge $Q$ due to the other two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $m ^ { 2 } / C ^ { 2 }$ )

Two point charges each experience a $1 - \mathrm { N }$ electrostatic force when they are $2 \mathrm {~cm}$ apart. If they are moved to a new separation of $8 \mathrm {~cm}$ , what is the magnitude of the electric force on each of them?

A small glass bead has been charged to $1.9 \mathrm { nC }$ . What is the strength of the electric field $2.0 \mathrm {~cm}$ from the center of the bead? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$