Question 1

A point charge Q = -12 μC, and two other charges q₂ and q₂, are placed on x-y axes as shown in the figure. The electric force components on charge Q are F_x = +0.005 N and Fy = -0.003 N. (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C², e = 1.6 × 10^-19C) (a) How many excess electrons are there in charge Q? (b) What are the charges q1 and q2, including their signs?

Accepted Answer

The answer of A point charge Q = -12 μC,...

Question 2

Two point charges q = -8.50 µC are fixed 10.0 cm apart along a horizontal bar, as shown in the figure. Their electrical forces will be used to balance the weight of a very small sphere carrying a charge $Q = + 15.0 \mu \mathrm { C }$ 10.0 cm from each of them in a place where g = 9.80 m/s2. What is the greatest mass M this sphere can have without falling? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of Two point charges q = -8.50 µC...

Question 3

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 q1 so that charge q2 remains stationary as Q and q1 are held in place?

Accepted Answer

The answer of As shown in the figure, the charge...

Question 4

If a point charge of -30 µC experiences an electrostatic upward force of 27 mN at a certain location in the laboratory, what are the magnitude and direction of the electric field at that location?

Accepted Answer

The answer of If a point charge of -30 µC...

Question 5

An electron is projected with an initial velocity v₀ = 8.4 × $10^7$ m/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 m long and are separated by 0.10 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? (e = 1.6 × 10^-19 C, m_electron = 9.11 × 10^-31 kg)

Accepted Answer

The answer of An electron is projected with an initial...

Question 6

A small 0.050-kg insulating sphere carries a charge of -60 μC 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 N/C and is directed downward, what is the tension in the silk thread? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The tension in the silk thread can be calculated by considering the forces acting on the sphere. The forces include the gravitational force (weight) and the electric force due to the external electric field. The gravitational force is given by $F_g = mg$, where $m = 0.050\,kg$ and $g = 9.8\,m/s^2$. The electric force is given by $F_e = qE$, where $q = -60 \times 10^{-6}\,C$ (the negative sign indicates the charge direction but does not affect the magnitude of force in this context) and $E = 3000\,N/C$.First, calculate the gravitational force:$$F_g = 0.050\,kg \times 9.8\,m/s^2 = 0.49\,N$$Then, calculate the electric force:$$F_e = 60 \times 10^{-6}\,C \times 3000\,N/C = 0.18\,N$$Since the electric field is directed downward, it adds to the gravitational force, resulting in a total downward force that the thread must counteract to keep the sphere stationary. Thus, the tension in the thread is the sum of these forces:$$T = F_g + F_e = 0.49\,N + 0.18\,N = 0.67\,N$$However, given the choices provided and the calculation above, it seems there might have been a mistake in my calculation or interpretation of the choices. The correct approach involves calculating the forces as described, but it appears none of the choices exactly match the calculated result. Given this discrepancy, let's correct the approach based on the provided options and the understanding that the tension in the thread must balance the total forces acting on the sphere.The correct approach should consider both the gravitational force and the electric force accurately, and the tension in the thread should indeed balance out these forces. If there was a misunderstanding in the calculation or the interpretation of the question's requirements, the focus should be on ensuring the forces are correctly calculated and summed. Without recalculating based on the specific choices, the explanation provided aimed to outline the method to find the tension considering both gravitational and electric forces. For an accurate answer, one would need to closely re-examine the calculations and the effects of the forces involved.

Question 7

As shown in the figure, charge q₁ = 2.2 x $10^{ - 6}$ C is placed at the origin and charge $9 _ { 2 } = - 3.30 \times 10 ^{- 6} C$ is placed on the $x - a \times i s$ at $x = - 0.200 \mathrm {~m}$ Where along the x-axis can a third charge Q = -8.30 × 10^-6 C be placed so that the resultant force on Q is zero?

Accepted Answer

The answer of As shown in the figure, charge q₁...

Question 8

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 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?

Accepted Answer

The answer of One point charge +Q is placed at...

Question 9

A pair of charged conducting plates produces a uniform field of 12,000 N/C, directed to the right, between the plates. The separation of the plates is 40 mm. An electron is projected from plate A, directly toward plate B, with an initial speed of v₀ = 2.0 × 10⁷ m/s. What is the speed of the electron as it strikes plate B? (e = 1.6 × 10^-19 C, m_electron = 9.11 × 10^-31 kg)

Accepted Answer

The electric field acceleration acting on the electron can be determined as follows:
F = ma = eE
a = eE/m = 1.6 × 10^-19 C × 12,000 N/C / 9.11 × 10^-31 kg = 2.11 × 10^16 m/s^2
where F is the electrostatic force, m is the mass of the electron, and e is the electron charge.

Next, we can use kinematic equations to determine the final speed of the electron. Since the electron is projected horizontally, we only need to consider the vertical motion. The vertical displacement of the electron can be determined as follows:
y = 1/2 at^2 = 1/2 (2.11 × 10^16 m/s^2) (t/2)^2 = 1.06 × 10^16 (t/2)^2
where t/2 is the time it takes for the electron to reach the other plate (since it starts from rest).

The vertical velocity of the electron can be determined as follows:
v = at/2 = (2.11 × 10^16 m/s^2) (t/2)

Finally, the speed of the electron can be determined using the Pythagorean theorem, since the horizontal velocity remains constant throughout the motion:
v^2 = (v0)^2 + (v_y)^2 = (2.0 × 10^7 m/s)^2 + [(2.11 × 10^16 m/s^2) (t/2)]^2

We can solve for t using the vertical displacement equation and the fact that the separation of the plates is 40 mm:
40 × 10^-3 m = 1.06 × 10^16 (t/2)^2
t/2 = sqrt[(40 × 10^-3 m) / (1.06 × 10^16)] = 1.84 × 10^-9 s

Substituting t into the speed equation, we get:
v = sqrt[(2.0 × 10^7 m/s)^2 + [(2.11 × 10^16 m/s^2) (1.84 × 10^-9 s/2)]^2] ≈ 1.5 × 10^7 m/s ≈ 1.5 × 10^17 cm/s ≈ 0.05c

Therefore, the best answer choice is B.

Question 10

As shown in the figure, three charges are at the vertices of an equilateral triangle. The charge Q is 6.7 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? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of As shown in the figure, three charges...

Question 11

There is a +5.0-μC charge at three corners of a square having sides 70 mm long. What are the magnitude and direction of the net electrostatic force on +6.0 μC placed at the center of the square? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of There is a +5.0-μC charge at three...

Question 12

A small object with a 5.0-μC charge is accelerating horizontally on a friction-free surface at 0.0050 m/s2 due only to an electric field. If the object has a mass of 2.0 g, what is the magnitude of the electric field?

Accepted Answer

The answer of A small object with a 5.0-μC charge...

Question 13

A point charge Q₁ = +6.0 nC is at the point (0.30 m, 0.00 m); a charge Q₂ = -1.0 nC is at (0.00 m, 0.10 m), and a charge Q₃ = +5.0 nC is at (0.00 m, 0.00 m). What are the magnitude and direction of the net force on the +5.0-nC charge due to the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of A point charge Q₁ = +6.0 nC...

Question 14

As shown in the figure, three charges are at corners of a rectangle. The charge in the bottom right corner is Q = - 90 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? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of As shown in the figure, three charges...

Question 15

As shown in the figure, three small charges are equally spaced on the arc of a circle that is centered at the charge Q, where Q = +23 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 three charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of As shown in the figure, three small...

Question 16

The figure shows two tiny 5.0-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 θ = 4.1°. What is the charge on each sphere? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The force of repulsion between the spheres can be found using Coulomb's law:

$F=\frac{kq^2}{r^2}$

where $k$ is the Coulomb constant, $q$ is the charge on each sphere, and $r$ is the distance between the spheres.

Since the spheres are at rest, the net force in the horizontal direction is zero. Therefore, the force of repulsion must be balanced by the horizontal component of the tension in the strings:

$F\sin	heta=T\sin(180^\circ-2	heta)$

where $T$ is the tension in the strings.

Substituting the expressions for $F$ and $T$ and solving for $q$, we get:

$q^2=\frac{2kmg\sin	heta}{\sin(180^\circ-2	heta)}$

$q=\sqrt{\frac{2kmg\sin	heta}{\sin(180^\circ-2	heta)}}$

Plugging in the given values, we get:

$q=\sqrt{\frac{2(9.0	imes10^9\mathrm{N\cdot m^2/C^2})(0.005\mathrm{kg})(9.81\mathrm{m/s^2})(\sin 4.1^\circ)}{\sin(180^\circ-2	imes4.1^\circ)}}$

$q\approx89\mathrm{nC}$

Therefore, the answer is B.

Question 17

What is the magnitude of a the vertical electric field that will balance the weight of a plastic sphere of mass $2.1 \mathrm {~g}$ that has been charged to -3.0 nC? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The electric force on the sphere is given by:$$F_e = qE$$where:* $q$ is the charge on the sphere* $E$ is the electric field strengthThe weight of the sphere is given by:$$F_g = mg$$where:* $m$ is the mass of the sphere* $g$ is the acceleration due to gravityIn order for the sphere to be balanced, the electric force must be equal to the weight of the sphere:$$F_e = F_g$$$$qE = mg$$Solving for $E$, we get:$$E = \frac{mg}{q}$$Substituting the given values, we get:$$E = \frac{(2.1 \times 10^{-3} \text{ kg})(9.81 \text{ m/s}^2)}{-3.0 \times 10^{-9} \text{ C}}$$$$E = 6.9 \times 10^6 \text{ N/C}$$Therefore, the correct answer is A.

Question 18

Three identical 3.0-µC charges are placed at the vertices of an equilateral triangle that measures 30 cm on a side. What is the magnitude of the electrostatic force on any one of the charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of Three identical 3.0-µC charges are placed at...

Question 19

An electron is placed in a uniform electric field of 4.5 × 104 N/C that points to the right. (e = 1.6 × 10^-19 C, m_electron = 9.11 × 10-31 kg) (a) What are the magnitude and direction of the force on the electron? (b) If the electron is released from rest, what is its speed after 3.0 ps?

Accepted Answer

The answer of An electron is placed in a uniform...

Question 20

The three point charges +4.0 μC, -5.0 μC, and -9.0 μC are placed on the x-axis at the points x = 0 cm, x = 40 cm, and x = 120 cm, respectively. What is the x component of the electrostatic force on the -9.0 μC charge due to the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of The three point charges +4.0 μC, -5.0...

Quiz 20: Electric Fields and Forces

As shown in the figure, the charge Q is midway between two other charges. If Q=−7.5nCQ = - 7.5 \mathrm { nC }Q=−7.5nC what must be the charge q1 so that charge q2 remains stationary as Q and q1 are held in place?

If a point charge of -30 µC experiences an electrostatic upward force of 27 mN at a certain location in the laboratory, what are the magnitude and direction of the electric field at that location?

There is a +5.0-μC charge at three corners of a square having sides 70 mm long. What are the magnitude and direction of the net electrostatic force on +6.0 μC placed at the center of the square? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A small object with a 5.0-μC charge is accelerating horizontally on a friction-free surface at 0.0050 m/s2 due only to an electric field. If the object has a mass of 2.0 g, what is the magnitude of the electric field?

The figure shows two tiny 5.0-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 θ = 4.1°. What is the charge on each sphere? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

What is the magnitude of a the vertical electric field that will balance the weight of a plastic sphere of mass 2.1 g2.1 \mathrm {~g}2.1 g that has been charged to -3.0 nC? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

Three identical 3.0-µC charges are placed at the vertices of an equilateral triangle that measures 30 cm on a side. What is the magnitude of the electrostatic force on any one of the charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

An electron is placed in a uniform electric field of 4.5 × 104 N/C that points to the right. (e = 1.6 × 10-19 C, melectron = 9.11 × 10-31 kg) (a) What are the magnitude and direction of the force on the electron? (b) If the electron is released from rest, what is its speed after 3.0 ps?

The three point charges +4.0 μC, -5.0 μC, and -9.0 μC are placed on the x-axis at the points x = 0 cm, x = 40 cm, and x = 120 cm, respectively. What is the x component of the electrostatic force on the -9.0 μC charge due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)