Question 1

Two tiny beads,each of mass 3.2 g,carry equal-magnitude charges.When they are placed 6.4 cm apart and released in outer space,they begin to accelerate toward each other at 538 m/s².What is the magnitude of the charge on each bead? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

Firstly, we can use the equation for electrostatic force between two point charges: 
F = k*q1*q2/r^2
where F is the force, k is Coulomb's constant (1/4πε0), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
We can rearrange this equation to solve for the charges:
q = sqrt(F*r^2/k)
Now we can substitute in the given values:
F = m*a = 2*3.2*10^-3 kg * 538 m/s^2 = 3.45 N
r = 6.4 cm = 0.064 m
k = 9.0*10^9 N·m^2/C^2
Plugging these values into the equation for q, we get:
q = sqrt((2*3.45*0.064^2)/(9.0*10^9)) = 8.9*10^-7 C = 890 nC
Therefore, the answer is D.

Question 2

Three point charges are placed on the x-axis,as follows.A charge of +2.0 μC is at the origin,a charge of -2.0 μC is at x = 50 cm,and a charge of +4.0 μC is at x = 100 cm.What are the magnitude and direction of the net electrostatic force exerted on the charge at the origin by the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of Three point charges are placed on the...

Question 3

Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at $414 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The electric force $ F $ can be calculated using $ F = ma $, where $ m = 1.0 \times 10^{-3} $ kg and $ a = 414 $ m/s². Then, using Coulomb's law $ F = \frac{kq^2}{r^2} $, solve for $ q $ with $ r = 0.02 $ m and $ k = 9.0 \times 10^9 $ N∙m²/C². The calculation gives $ q \approx 140 $ nC.

Question 4

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 exerted on the +5.0-nC charge by 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 5

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 exerted 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^-19 C) (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,and...

Question 6

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 exerted 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 7

Suppose you wanted to hold up an electron against the gravitational force by the attraction of a fixed proton some distance above it.How far above the electron would the proton have to be? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²,e = 1.6 × 10^-19 C,m_proton = 1.67 × 10^-27 kg,m_electron = 9.11 × 10^-31 kg)

Accepted Answer

The answer of Suppose you wanted to hold up an...

Question 8

Two tiny particles having charges of +5.00 μC and +7.00 μC are placed along the x-axis.The +5.00-µC particle is at x = 0.00 cm,and the other particle is at x = 100.00 cm.Where on the x-axis must a third charged particle be placed so that the net electrostatic force exerted on it by the other two particles is zero?

Accepted Answer

The answer of Two tiny particles having charges of +5.00...

Question 9

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

Accepted Answer

Let the third positive charge be q3 and let it be placed at a distance x from the origin.

The electric force exerted on q3 due to the charge +2q is:

F1 = k(2q)(q3) / x^2

The electric force exerted on q3 due to the charge -q is:

F2 = k(-q)(q3) / (2a - x)^2

The net electric force on q3 is zero when F1 = F2. Substituting the expressions for F1 and F2, we get:

k(2q)(q3) / x^2 = k(-q)(q3) / (2a - x)^2

Simplifying and solving for x, we get:

x = (4/3) a

Therefore, the third positive charge should be placed at a distance of (4/3) a from the origin, which is equivalent to 6.8a. Therefore, the correct answer 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 exerted on the charge Q by 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 are...

Question 11

Two tiny particles having charges of +7.00 μC and -9.00 μC are placed along the y-axis.The +7.00-µC particle is at y = 0.00 cm,and the other particle is at y = 40.00 cm.Where must a third charged particle be placed along the y-axis so that the net electric force exerted on it by the other two particles is zero?

Accepted Answer

The answer of Two tiny particles having charges of +7.00...

Question 12

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 force that Earth exerts on 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 13

As shown in the figure,the charge Q is midway between two other charges.If $Q = - 7.5 n C$ 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 Q...

Question 14

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 exerted on the charge Q by 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 charges...

Question 15

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 exerted on Q by 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 are...

Question 16

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 net electrostatic force exerted on the -9.0 μC charge by 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 μC,and...

Question 17

As shown in the figure,charge q₁ = 2.2 x $10^{ - 6}$ C is placed at the origin and charge $q _ { 2 } = - 3.30 \times 10 ^ { - 6 } C$ is placed on the $x - a x 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 exerted on Q is zero?

Accepted Answer

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

Question 18

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 is exerted 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 is exerted on the center charge now?

Accepted Answer

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

Question 19

Three point charges are located on the x-axis at the following positions: Q₁ = +2.00 μC is at x = 1.00 m,Q₂ = +3.00 μC is at x = 0.00,and Q₃ = -5.00 μC is at x = -1.00 m.What is the magnitude of the electric force exerted on Q2? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Accepted Answer

The forces on Q2 due to Q1 and Q3 are calculated using Coulomb's law. The force due to Q1 is repulsive and the force due to Q3 is attractive. The net force is the sum of these forces, which results in a magnitude of 0.189 N.

Question 20

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 exerted 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...

Quiz 15: Electric Charge force and Energy

Two tiny beads,each of mass 3.2 g,carry equal-magnitude charges.When they are placed 6.4 cm apart and released in outer space,they begin to accelerate toward each other at 538 m/s2.What is the magnitude of the charge on each bead? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

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 exerted on +6.0 μC placed at the center of the square? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

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

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

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 net electrostatic force exerted on the -9.0 μC charge by the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

Three point charges are located on the x-axis at the following positions: Q1 = +2.00 μC is at x = 1.00 m,Q2 = +3.00 μC is at x = 0.00,and Q3 = -5.00 μC is at x = -1.00 m.What is the magnitude of the electric force exerted on Q2? (k = 1/4πε0 = 8.99 × 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 exerted on any one of the charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)