Exam 16: Electric Charge and Electric Field

Two $10 \phi$ coins (dimes) carrying identical charges are lying $2.5 \mathrm {~m}$ apart on a table. If each of these coins experiences an electrostatic force of magnitude $2.0 \mathrm {~N}$ due to the other coin, how large is the charge on each coin? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Two tiny particles having charges of $+ 5.00 \mu \mathrm { C }$ and $+ 7.00 \mu \mathrm { C }$ are placed along the $x$ -axis. The $+ 5.00 - \mu \mathrm { C }$ particle is at $x = 0.00 \mathrm {~cm}$ , and the other particle is at $x = 100.00 \mathrm {~cm}$ . Where on the $x$ -axis must a third charged particle be placed so that it does not experience any net electrostatic force due to the other two particles?

When $1.0 - \mu \mathrm { C }$ point charge is $15 \mathrm {~m}$ from a second point charge, the force each one experiences a force of $1.0 \mu \mathrm { N }$ . What is the magnitude of the second charge? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

An electric dipole consists of charges of $\pm 6.00 \mu \mathrm { C }$ that are $10.0 \mathrm {~cm}$ apart, as shown in the figure. Find the magnitude and direction of the electric field this dipole produces at point $\mathrm { P }$ , which is $7.00 \mathrm {~cm}$ from each charge. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Three equal-magnitude point charges of varying signs 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?

Three equal-magnitude point charges of varying signs are placed at 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?

A tiny 0.0250- $\mu \mathrm { g }$ oil drop containing 15 excess electrons is suspended between two horizontally closely-spaced metal plates that carry equal but opposite charges on their facing surfaces. The plates are both circular with a radius of $6.50 \mathrm {~cm} . \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times \right.$ $\left. 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right)$ (a) How much excess charge must be on each plate to hold the oil drop steady? (b) Which plate must be positive, the upper one or the lower one?

Two point charges, $Q _ { 1 }$ and $Q _ { 2 }$ , are separated by a distance $R$ . If the magnitudes of both charges are doubled and their separation is also doubled, what happens to the electrical force that each charge exerts on the other one?

Suppose you wanted to hold up an electron against the force of gravity by the attraction of a fixed proton some distance above it. How far above the electron would the proton have to be? $( k = 1 / 4 \pi$ $\left. \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

Which one of the arrows shown in the figure best represents the direction of the electric field between the two uniformly charged metal plates?

Two stationary point charges $q _ { 1 }$ and $q _ { 2 }$ are shown in the figure along with a sketch of some field lines representing the electric field produced by them. What can you deduce from the sketch?

An electron and a proton are released simultaneously from rest and start moving toward each other due to their electrostatic attraction, with no other forces present. Which of the following statements are true just before they are about to collide? (There could be more than one correct choice.)

Gaussian surfaces $A$ and B enclose the same positive charge $+ Q$ . The area of Gaussian surface A is three times larger than that of Gaussian surface B. The electric flux through Gaussian surface $A$ is

What is the magnitude of the electric field $2.8 \mathrm {~cm}$ from a tiny object that carries an excess charge of $- 16 \mathrm { nC } ? \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A small object with a $5.0 - \mu \mathrm { C }$ charge is accelerating horizontally on a friction-free surface at $0.0050$ $\mathrm { m } / \mathrm { s } 2$ due only to an electric field. If the object has a mass of $2.0 \mathrm {~g}$ , what is the magnitude of the electric field?

In the figure, a conducting sphere of radius $r _ { 1 } = 0.050 \mathrm {~m}$ is placed at the center of a spherical conducting shell of inner radius $r _ { 2 } = 0.100 \mathrm {~m}$ and outer radius $r _ { 3 } = 0.140 \mathrm {~m}$ . The inner sphere carries an excess charge of $- 4.0 \mathrm { nC }$ . The outer spherical shell carries a net excess charge of $3.0 \mathrm { nC }$ . Calculate the magnitude of the electric field at the following distances $r$ from the center of the spheres. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$ (a) $r = 0.075 \mathrm {~m}$ (in the air space between spheres), (b) $r = 0.120 \mathrm {~m}$ (in the metal of the spherical shell), and (c) $r = 0.200 \mathrm {~m}$ (outside the spherical shell).

If a point charge of $- 30 \mu \mathrm { C }$ experiences an electrostatic upward force of $27 \mathrm { mN }$ at a certain Iocation in the laboratory, what are the magnitude and direction of the electric field at that location?

Three equal positive point charges $+ q$ are placed at 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?

The electric field at a point $2.8 \mathrm {~cm}$ from a small object points toward the object with a strength of $180,000 \mathrm {~N} / \mathrm { C }$ . What is the object's charge $\mathrm { q }$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

As shown in the figure, the charge $Q$ is midway between two other charges. If $Q = - 7.5 \mathrm { nC }$ , what must be the charge $q 1$ so that charge $q 2$ remains stationary as $Q$ and $q 1$ are held in place?