Question 1

Imagine that we place a dipole a distance $r$ from a neutral atom, as shown below.
 
-(b) Use figure E2.12 to specify the direction of the net force that the neutral atom exerts on the dipole. (Hint: Think of any dipole(s) as independent charged particles.
A) A
B) B
C) C
D) D
E) Zero
F) Other
G) AA
H) BB
I) $\mathrm{CC}$
J) DD

Accepted Answer

The answer of Imagine that we place a dipole a...

Question 2

If the electric field at any point inside a conductor is nonzero, the metal is not in static equilibrium.

Accepted Answer

In a conductor at static equilibrium, the electric field inside the conductor is zero because charges redistribute themselves on the surface of the conductor until the internal electric field is nullified.

Question 3

Imagine a neutral atom near an infinite charged plane. The neutral atom will be polarized by the plane's field.

Accepted Answer

The answer of Imagine a neutral atom near an infinite...

Question 4

Imagine a spherical shell with a uniformly distributed negative charge, as shown below. What are the directions of the field vectors created by that shell at the two points shown?
 
-(a) What is the direction at point $P_{1}$ just inside the shell?
A) A
B) B
C) C
D) D
E) zero
F) other
G) AA
H) BB
I) $\mathrm{CC}$
J) DD

Accepted Answer

The electric field inside a conductor in electrostatic equilibrium is zero. Since point $P_{1}$ is just inside the shell, the electric field and thus the direction of any force/electric field would be zero.

Question 5

Imagine a spherical shell with a uniformly distributed negative charge, as shown below. What are the directions of the field vectors created by that shell at the two points shown?
 
-(b) What is the direction at point $P_{2}$ just outside the shell?
A) A
B) B
C) C
D) D
E) zero
F) other
G) AA
H) BB
I) $\mathbf{C C}$
J) DD

Accepted Answer

The direction of the electric field just outside a charged shell is perpendicular to the surface, pointing away from the shell if it's positively charged, or towards it if negatively charged. This is represented by the double arrow in option I ($\mathbf{C C}$), indicating a direction perpendicular to the surface at point $P_{2}$.

Question 6

Imagine that we place a spherical shell with a uniformly distributed positive charge $Q$ and a particle with a negative charge $-4 Q$ as shown below. What are the directions of the total electric field vectors at the two points shown?
 
-(a) What is the direction at point $P_{1}$ at the shell's center?
A) A
B) B
C) C
D) D
E) zero
F) other
G) AA
H) BB
I) $\mathbf{C C}$
J) DD

Accepted Answer

The answer of Imagine that we place a spherical shell...

Question 7

Imagine that we place a spherical shell with a uniformly distributed positive charge $Q$ and a particle with a negative charge $-4 Q$ as shown below. What are the directions of the total electric field vectors at the two points shown?
 
-(b) What is the direction at point $\mathrm{P}_{2}$ ?
A) A
B) B
C) C
D) D
E) zero
F) other
G) AA
H) BB
I) $\mathrm{CC}$
J) DD

Accepted Answer

At point $P_2$, the direction is zero because this typically indicates a point of equilibrium or a stationary point where the direction or magnitude of a vector quantity (like velocity, force, etc.) is zero.

Question 8

Consider two concentric spherical shells, one with radius $R$ and one with radius $2 R$. Both have the same uniformly distributed charge $Q$. Let $E_{0} \equiv Q /\left(4 \pi \varepsilon_{0} R^{2}\right)$. Which of the values below is closest to the magnitude of the electric field vector created by these shells at a point $P$ just barely inside the outer shell?
A) zero
B) $\frac{1}{4} E_{0}$
C) $\frac{1}{2} E_{0}$
D) $E_{0}$
E) $2 E_{0}$
F) $4 E_{0}$
G) Other

Accepted Answer

The answer of Consider two concentric spherical shells, one with...

Question 9

Consider a solid sphere with radius $R$ with a charge uniformly spread throughout its volume. The magnitude of the sphere's electric field is $\left|\vec{E}_{1}\right|$ at a point $P_{1}$ on the sphere's surface and is $\left|\vec{E}_{2}\right|$ at a point $P_{2}$ at a distance $\frac{1}{2} R$ from the sphere's center. In the relationship $\left|\vec{E}_{1}\right|=b\left|\vec{E}_{2}\right|$, what is the value of $b$ ?
A) 0
B) 1
C) 2
D) 4
E) 8
F) Other

Accepted Answer

The electric field inside a uniformly charged sphere increases linearly with distance from the center, reaching its maximum at the surface. At a distance $r$ from the center, the magnitude of the electric field is given by $\left|\vec{E}\right| = \frac{1}{4\pi\epsilon_0} \frac{Q}{R^3} r$ for $r \leq R$, where $Q$ is the total charge, $R$ is the radius of the sphere, and $\epsilon_0$ is the vacuum permittivity. At the surface ($r = R$), this becomes $\left|\vec{E}_1\right| = \frac{1}{4\pi\epsilon_0} \frac{Q}{R^2}$. At a distance $\frac{1}{2}R$ from the center, the electric field is $\left|\vec{E}_2\right| = \frac{1}{4\pi\epsilon_0} \frac{Q}{R^3} \left(\frac{1}{2}R\right) = \frac{1}{2} \frac{1}{4\pi\epsilon_0} \frac{Q}{R^2}$. Therefore, $\left|\vec{E}_1\right| = 2\left|\vec{E}_2\right|$, making $b = 2$.

Question 10

The finite wire shown below has a uniformly distributed negative charge. Which of the arrows below is closest to the direction of the field vector that the wire produces at point $P$ ? (Point to a letter on the back cover with two fingers to specify a double-letter answer.)

A) A
B) B
C) C
D) D
E) AA
F) BB
G) CC
H) DD

Accepted Answer

The answer of The finite wire shown below has a...

Question 11

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified?

-(a) At point $P 1$ a small distance above the disk's center?
A) A
B) B
C) C
D) D
E) AA
F) BB
G) CC
H) DD

Accepted Answer

The answer of The finite disk shown below has a...

Question 12

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified?

-(b) At point $P 2$ ?
A) A
B) B
C) C
D) D
E) AA
F) BB
G) CC
H) DD

Accepted Answer

The correct answer is DD because at point P2, the value of the function is 4.

Question 13

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified?

-(c) At point $P 3$ ?
A) A
B) B
C) C
D) D
E) AA
F) BB
G) CC
H) DD

Accepted Answer

The answer of The finite disk shown below has a...

Question 14

The units of the electric field $\vec{E}$ are N/C. We can alternatively say the field has units of $V / m$.

Accepted Answer

The electric field $\vec{E}$ is defined as the force per unit charge, giving it units of N/C. It can also be described in terms of the potential difference (voltage, V) per unit distance (m), leading to units of $V/m$, due to the relationship between electric field and electric potential difference.

Question 15

A single particle can have potential energy.

Accepted Answer

The answer of A single particle can have potential energy....

Question 16

Even if we define the potential to be zero at infinity, the potential created by a charge distribution can be negative at another point.

Accepted Answer

The potential at a point due to a charge distribution is determined by the work done to bring a unit positive charge from infinity to that point. If the point is closer to negative charges or within a distribution of opposite charge, the potential can indeed be negative, reflecting that work is done by the electric field on the unit charge.

Question 17

Consider a point $P$ midway between two identical charged particles. The potential $\phi$ at point $P$ is zero.

Accepted Answer

The potential at point $P$ is not zero because electric potential is a scalar quantity and adds algebraically. Since the charges are identical and $P$ is equidistant from both, their potentials at $P$ will add, not cancel out.

Question 18

Consider a point $P$ midway between two particles, one with charge $-q$ and one with charge $q$. The electric field vector $\vec{E}$ at point $P$ is zero.

Accepted Answer

The electric field due to a positive charge points away from the charge, and the electric field due to a negative charge points towards the charge. At point $P$, which is equidistant from both charges, the electric fields due to each charge are equal in magnitude but opposite in direction, thus canceling each other out, resulting in a net electric field of zero.

Question 19

Consider a point $P$ midway between two identical charged particles. The electric field vector $\vec{E}$ at point $P$ is zero

Accepted Answer

At point $P$, which is exactly midway between two identical charges, the electric field vectors due to each charge are equal in magnitude but opposite in direction, thus canceling each other out, resulting in a net electric field of zero.

Question 20

Consider a point $P$ midway between two identical charged particles. The electric field vector $\vec{E}$ at point $P$ is zero

Accepted Answer

The answer of Consider a point $P$ midway between two...

Quiz 4: Electricity and Magnetism Are Unified

If the electric field at any point inside a conductor is nonzero, the metal is not in static equilibrium.

Imagine a neutral atom near an infinite charged plane. The neutral atom will be polarized by the plane's field.

The finite wire shown below has a uniformly distributed negative charge. Which of the arrows below is closest to the direction of the field vector that the wire produces at point $P$ ? (Point to a letter on the back cover with two fingers to specify a double-letter answer.)

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(a) At point $P 1$ a small distance above the disk's center?

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(b) At point $P 2$ ?

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(c) At point $P 3$ ?

The units of the electric field $\vec{E}$ are N/C. We can alternatively say the field has units of $V / m$ .

A single particle can have potential energy.

Even if we define the potential to be zero at infinity, the potential created by a charge distribution can be negative at another point.

Consider a point $P$ midway between two identical charged particles. The potential $\phi$ at point $P$ is zero.

Consider a point $P$ midway between two particles, one with charge $-q$ and one with charge $q$ . The electric field vector $\vec{E}$ at point $P$ is zero.

Consider a point $P$ midway between two identical charged particles. The electric field vector $\vec{E}$ at point $P$ is zero

Consider a point $P$ midway between two identical charged particles. The electric field vector $\vec{E}$ at point $P$ is zero

Quiz 4: Electricity and Magnetism Are Unified

Imagine that we place a dipole a distance rrr from a neutral atom, as shown below. -(b) Use figure E2.12 to specify the direction of the net force that the neutral atom exerts on the dipole. (Hint: Think of any dipole(s) as independent charged particles.

If the electric field at any point inside a conductor is nonzero, the metal is not in static equilibrium.

Imagine a neutral atom near an infinite charged plane. The neutral atom will be polarized by the plane's field.

Imagine a spherical shell with a uniformly distributed negative charge, as shown below. What are the directions of the field vectors created by that shell at the two points shown? -(a) What is the direction at point P1P_{1}P1​ just inside the shell?

Imagine a spherical shell with a uniformly distributed negative charge, as shown below. What are the directions of the field vectors created by that shell at the two points shown? -(b) What is the direction at point P2P_{2}P2​ just outside the shell?

The finite wire shown below has a uniformly distributed negative charge. Which of the arrows below is closest to the direction of the field vector that the wire produces at point PPP ? (Point to a letter on the back cover with two fingers to specify a double-letter answer.)

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(a) At point P1P 1P1 a small distance above the disk's center?

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(b) At point P2P 2P2 ?

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(c) At point P3P 3P3 ?

The units of the electric field E⃗\vec{E}E are N/C. We can alternatively say the field has units of V/mV / mV/m .

A single particle can have potential energy.

Even if we define the potential to be zero at infinity, the potential created by a charge distribution can be negative at another point.

Consider a point PPP midway between two identical charged particles. The potential ϕ\phiϕ at point PPP is zero.

Consider a point PPP midway between two particles, one with charge −q-q−q and one with charge qqq . The electric field vector E⃗\vec{E}E at point PPP is zero.

Consider a point PPP midway between two identical charged particles. The electric field vector E⃗\vec{E}E at point PPP is zero

Consider a point PPP midway between two identical charged particles. The electric field vector E⃗\vec{E}E at point PPP is zero

The finite wire shown below has a uniformly distributed negative charge. Which of the arrows below is closest to the direction of the field vector that the wire produces at point $P$ ? (Point to a letter on the back cover with two fingers to specify a double-letter answer.)

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(a) At point $P 1$ a small distance above the disk's center?

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(b) At point $P 2$ ?

The finite disk shown below has a uniformly distributed positive charge. Which of the arrows in figure E2.12 best indicates the direction of the electric field vector that the plate produces at the points specified? -(c) At point $P 3$ ?

The units of the electric field $\vec{E}$ are N/C. We can alternatively say the field has units of $V / m$ .

Consider a point $P$ midway between two identical charged particles. The potential $\phi$ at point $P$ is zero.

Consider a point $P$ midway between two particles, one with charge $-q$ and one with charge $q$ . The electric field vector $\vec{E}$ at point $P$ is zero.

Consider a point $P$ midway between two identical charged particles. The electric field vector $\vec{E}$ at point $P$ is zero

Consider a point $P$ midway between two identical charged particles. The electric field vector $\vec{E}$ at point $P$ is zero