Exam 16: Electric Charge and Electric Field

Two very small plastic balls of equal mass are released from rest. One of them carries $+ 10 \mu \mathrm { C }$ of excess charge and the other one carries $+ 1 \mu \mathrm { C }$ of charge. No other charges or fields are present. Which of the following statements are true about them as they move away from each other? (There may be more than one correct choice.)

As shown in the figure, charge $q _ { 1 } = 2.2 \times 10 ^ { - 6 } \mathrm { C }$ is placed at the origin and charge $q _ { 2 } = - 3.30 \times 10 ^ { - 6 } \mathrm { C }$ is placed on the $x$ -axis, at $x = - 0.200 \mathrm {~m}$ . Where along the $x$ -axis can a third charge $Q = - 8.30 \times 10 ^ { - 6 } \mathrm { C }$ be placed so that the resultant force on $Q$ is zero?

A small charged plastic ball is vertically above another charged small ball in a frictionless test tube as shown in the figure. The balls are in equilibrium a distance $d$ apart. If the charge on each ball is doubled, the equilibrium distance between the balls in the test tube would become

Three equal negative point charges $- q$ are placed at three of the corners of a square of side $d$ as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the vacant corner of the square?

Two electrons are $20.0 \mathrm {~mm}$ apart at closest approach. What is the magnitude of the maximum electric force that they exert on each other? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , k = 1 / 4 \pi \varepsilon _ { 0 } = 9.010 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A point charge $Q _ { 1 } = + 6.0 \mathrm { nC }$ is at the point $( 0.30 \mathrm {~m} , 0.00 \mathrm {~m} )$ ; a charge $Q _ { 2 } = - 1.0 \mathrm { nC }$ is at $( 0.00 \mathrm {~m} , 0.10 \mathrm {~m} )$ , and a charge $Q _ { 3 } = + 5.0 \mathrm { nC }$ is at $( 0.00 \mathrm {~m} , 0.00 \mathrm {~m} )$ . What are the magnitude and direction of the net force on the $+ 5.0 - \mathrm { nC }$ charge due to the other two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

The figure shows two tiny $5.0 - \mathrm { g }$ spheres suspended from very light $1.0$ -m-long threads. The spheres repel each other after each one is given the same positive charge and hang at rest when $\theta$ $= 4.1 ^ { \circ }$ . What is the charge on each sphere $? \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A nonconducting sphere of mass 18.5 kg and diameter 25.0 cm has 8.10 × 1015 electrons removed from it. The points of removal are spread uniformly throughout the volume of this sphere. A tiny neutral plastic ball of mass 0.120 g is placed just outside the surface of the large sphere and is then released. How many electrons must be removed from the plastic ball so that its initial acceleration just after being released will be 1525 m/s²? You $\text { can neglect gravity. } \left( e = 1.6 \times 10 ^ { - 19 } \mathrm { C } , k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A piece of plastic has a net charge of $+ 2.00 \mu \mathrm { C }$ . How many more protons than electrons does this piece of plastic have? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A hydrogen nucleus, which has a charge $+ e$ , is situated to the left of a carbon nucleus, which has a charge $+ 6 \mathrm { e }$ . Which statement is true?

Three equal negative point charges $- q$ are placed at three of the corners of a square of side $d$ as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the center of the square?

Two tiny particles carrying like charges of the same magnitude are $1.0 \mathrm {~mm}$ apart. If the electric force on one of them is $5.0 \mathrm {~N}$ , what is the magnitude of the charge on each of these particles? $( k =$ $1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

The three point charges $+ 4.0 \mu \mathrm { C } , - 5.0 \mu \mathrm { C }$ , and $- 9.0 \mu \mathrm { C }$ are placed on the $x$ -axis at the points $x = 0$ $\mathrm { cm } , x = 40 \mathrm {~cm}$ , and $x = 120 \mathrm {~cm}$ , respectively. What is the $x$ component of the electrostatic force on the $- 9.0 \mu \mathrm { C }$ charge due to the other two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Two small identically charged balls are a certain distance apart. The vectors in the figure show the magnitude and direction of the electrostatic force on each ball due to the other one. Suppose that the charge on the left ball is now doubled (represented by two plus signs). Which vector diagram below best represents the forces that now act on each of the two balls?

A particle with a charge of $+ 4.0 \mu \mathrm { C }$ has a mass of $5.0 \mathrm {~g}$ . What magnitude electric field directed upward will exactly balance the weight of the particle?

Three equal charges $+ Q$ are at three of the corners of a square of side $d$ . A fourth charge $+ Q$ of equal magnitude is at the center of the square as shown in the figure Which one of the arrows shown represents the net force acting on the charge at the center of the square?

A metal sphere of radius $10 \mathrm {~cm}$ carries an excess charge of $+ 2.0 \mu \mathrm { C }$ . What is the magnitude of the electric field $5.0 \mathrm {~cm}$ above the sphere's surface? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right.$ )

There is $\mathrm { a } + 5.0 - \mu \mathrm { C }$ charge at three corners of a square having sides $70 \mathrm {~mm}$ long. What are the magnitude and direction of the net electrostatic force on $+ 6.0 \mu \mathrm { C }$ placed at the center of the square? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A uniform electric field with a magnitude of $6 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { C }$ i is directed along the $+ x$ -axis. A cube having edges of length $0.1 \mathrm {~m}$ is oriented as shown in the figure. What is the electric flux passing through the shaded face of the cube?

The figure shows four Gaussian surfaces surrounding a distribution of charges. (a) Which Gaussian surfaces have an electric flux of $+ q / \varepsilon _ { 0 }$ through them? (b) Which Gaussian surfaces have no electric flux through them?