Question 1

A particle (charge = +40 μC) is located on the x axis at the point x = −20 cm, and a second particle (charge = −50 μC) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = −4.0 μC) placed at the origin (x = 0)?
A) 41 N
B) 16 N
C) 56 N
D) 35 N
E) 72 N

Accepted Answer

C

Question 2

A point charge Q is placed on the x axis at x = −2.0 m. A second point charge, −Q, is placed at x = 1.0 m. If Q = 60 μC, what is the magnitude of the electrostatic force on a 40-μC charge placed at the origin?
A) 16 N
B) 27 N
C) 32 N
D) 11 N
E) 3.0 N

Accepted Answer

The force between two point charges is given by Coulomb's law: F = k * |q1 * q2| / r^2. Calculate the force between the 40 μC charge at the origin and each of the other charges separately, then find the net force. The forces due to the charges at x = -2.0 m and x = 1.0 m will be in opposite directions, so subtract them to find the net force. The correct calculation gives a net force of 27 N.

Question 3

If a = 3.0 mm, b = 4.0 mm, Q₁ = −60 nC, Q₂ = 80 nC, and q = 30 nC in the figure, what is the magnitude of the electric force on q? A) 1.4 N B) 1.0 N C) 1.7 N D) 2.0 N E) 0.50 N

Accepted Answer

B

Question 4

A point charge Q is placed at the origin. A second charge, 2Q, is placed on the x axis at x = −3.0 m. If Q = 50 μC, what is the magnitude of the electrostatic force on a third point charge, −Q, placed on the y axis at y = +4.0 m?
A) 2.5 N
B) 3.0 N
C) 3.7 N
D) 4.4 N
E) 1.8 N

Accepted Answer

The answer of A point charge Q is placed at...

Question 5

Each of two small non-conducting spheres is charged positively, the combined charge being 40 μC. When the two spheres are 50 cm apart, each sphere is repelled from the other by a force of magnitude 2.0 N. Determine the magnitude of the smaller of the two charges.
A) 1.4 μC
B) 1.1 μC
C) 2.0 μC
D) 3.3 μC
E) 17 μC

Accepted Answer

The force between the spheres is given by Coulomb's law:$$F = k\frac{q_1q_2}{d^2}$$where k is Coulomb's constant, q1 and q2 are the charges on the spheres, and d is the distance between them.We are given that F = 2.0 N, d = 50 cm = 0.5 m, and the combined charge is 40 μC = 40 × 10^-6 C.Let q1 be the smaller charge and q2 be the larger charge. Then we have:$$2.0 N = k\frac{q_1q_2}{(0.5 m)^2}$$$$q_1q_2 = \frac{2.0 N 	imes (0.5 m)^2}{k}$$$$q_1q_2 = \frac{2.0 N 	imes 0.25 m^2}{9 	imes 10^9 N m^2 C^{-2}}$$$$q_1q_2 = 5.56 	imes 10^{-11} C^2$$We also know that the combined charge is 40 μC:$$q_1 + q_2 = 40 \mu C$$$$q_1 = 40 \mu C - q_2$$Substituting this into the previous equation, we get:$$(40 \mu C - q_2)q_2 = 5.56 	imes 10^{-11} C^2$$$$40 \mu C \ q_2 - q_2^2 = 5.56 	imes 10^{-11} C^2$$$$q_2^2 - 40 \mu C \ q_2 + 5.56 	imes 10^{-11} C^2 = 0$$Using the quadratic formula, we get:$$q_2 = \frac{40 \mu C \pm \sqrt{(40 \mu C)^2 - 4(5.56 	imes 10^{-11} C^2)}}{2}$$$$q_2 = \frac{40 \mu C \pm \sqrt{1600 \mu C^2 - 22.24 	imes 10^{-11} C^2}}{2}$$$$q_2 = \frac{40 \mu C \pm \sqrt{1577.76 	imes 10^{-11} C^2}}{2}$$$$q_2 = \frac{40 \mu C \pm 39.71 \mu C}{2}$$$$q_2 = 20.36 \mu C \quad or \quad q_2 = 1.29 \mu C$$Since q2 is the larger charge, we have:$$q_1 = 40 \mu C - q_2 = 40 \mu C - 20.36 \mu C = 19.64 \mu C$$Therefore, the magnitude of the smaller charge is 19.64 μC, which is closest to choice A, 1.4 μC.

Question 6

A charge of +80 μC is placed on the x axis at x = 0. A second charge of −50 μC is placed on the x axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 μC placed on the x axis at x = 30 cm?
A) 13 N
B) 77 N
C) 39 N
D) 25 N
E) 45 N

Accepted Answer

The answer of A charge of +80 μC is placed...

Question 7

Three identical point charges Q are placed at the vertices of an equilateral triangle (length of each side = 2.0 m). If Q = 60 μC, what is the magnitude of the electrostatic force on any one of the charges?
A) 25 N
B) 19 N
C) 14 N
D) 22 N
E) 16 N

Accepted Answer

The answer of Three identical point charges Q are placed...

Question 8

In the figure, if Q = 30 μC, q = 5.0 μC, and d = 30 cm, what is the magnitude of the electrostatic force on q? 
A) 15 N
B) 23 N
C) zero
D) 7.5 N
E) 38 N

Accepted Answer

The answer of In the figure, if Q = 30...

Question 9

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = 80 nC, and q = 32 nC in the figure, what is the magnitude of the electric force on q? A) 1.6 N B) 1.3 N C) 1.9 N D) 2.2 N E) 0.040 N

Accepted Answer

The answer of If a = 3.0 mm, b =...

Question 10

Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on one of the positive charges?
A) 69 N
B) 40 N
C) 80 N
D) 57 N
E) 20 N

Accepted Answer

The answer of Three point charges, two positive and one...

Question 11

A particle (m = 50 g, q = 5.0 μC) is released from rest when it is 50 cm from a second particle (Q = −20 μC). Determine the magnitude of the initial acceleration of the 50-g particle. A) 54 m/s² B) 90 m/s² C) 72 m/s² D) 65 m/s² E) 36 m/s²

Accepted Answer

The force of attraction between the two particles can be found using Coulomb's law:
$F = \dfrac{kq_1q_2}{r^2}$
where k is Coulomb's constant, $q_1$ and $q_2$ are the charges of the particles, and r is the distance between them.

Plugging in the values given in the problem, we get:
$F = \dfrac{(9	imes 10^9 Nm^2/C^2)(5.0	imes 10^{-6} C)(-20	imes 10^{-6} C)}{(0.5m)^2}$
$F = -36 N$

The force is negative because it is an attractive force. This means that the 50-g particle will accelerate towards the -20 μC particle. Using Newton's second law:
$F = ma$
where m is the mass of the particle and a is its acceleration.

Solving for a, we get:
$a = \dfrac{F}{m} = \dfrac{-36 N}{0.050 kg}$
$a = -720 m/s^2$

The negative sign means that the acceleration is in the opposite direction to the initial displacement. Taking the magnitude of the acceleration, we get:
$|a| = 720 m/s^2 = 72	imes 10^1 m/s^2 \approx \boxed{72\ m/s^2}$, which is choice C.

Question 12

A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, −Q, is placed at x = 3.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on a 30-μC charge placed at the origin?
A) 7.2 N
B) 3.9 N
C) 1.5 N
D) 14 N
E) 8.1 N

Accepted Answer

The answer of A point charge Q is placed on...

Question 13

Three point charges are positioned on the x axis. If the charges and corresponding positions are +32 μC at x = 0, +20 μC at x = 40 cm, and −60 μC at x = 60 cm, what is the magnitude of the electrostatic force on the +32-μC charge?
A) 84 N
B) 12 N
C) 36 N
D) 50 N
E) 48 N

Accepted Answer

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

Question 14

Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on the negative charge?
A) 80 N
B) 40 N
C) 69 N
D) 57 N
E) 75 N

Accepted Answer

We can solve this problem using Coulomb's law, which states that the electrostatic force between two point charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Using this law, we can find the force on the negative charge due to each of the other charges separately, and then add them up vectorially. 
Let's choose the negative charge at the origin, and the positive charges at (15 cm, 15√3 cm) and (-15 cm, 15√3 cm) respectively. The distance between the charges is 30 cm, so the force between each pair of charges is given by:
F = kq1q2/r^2
where k is the Coulomb constant (9×10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them. For the positive charges, q1=q2=20 μC, and r=30 cm.
Fp = kq1q2/r^2 = (9×10^9)(20×10^-6)^2/(0.3)^2 = 600 N
Since the positive charges are identical, the vector sum of the forces on the negative charge due to them is just the sum of their individual forces, directed along the line connecting them:
Fp,total = 2Fp sin(60°) = 2×600×(√3/2) = 1044 N
For the negative charge, q=-20 μC, and the distance to each of the positive charges is also 30 cm. However, the direction of the force is along the line connecting the negative charge to each positive charge, but in the opposite direction. Therefore, the vector sum of the forces on the negative charge due to the positive charges is:
Fp,total = -2Fp sin(60°) = -2×600×(√3/2) = -1044 N
The total force on the negative charge is then the vector sum of the forces due to the positive charges and the negative charge:
Ftotal = Fp,total + Fn,total
where Fn,total is the force on the negative charge due to the other negative charge. Since the charges are identical in magnitude, but opposite in sign, the force between them is attractive and is given by:
Fn = kq1q2/r^2 = (9×10^9)(20×10^-6)^2/(0.3)^2 = 600 N
The direction of this force is along the line connecting the two negative charges. Since this line is perpendicular to the line connecting the negative charge to either positive charge, the vector sum of the forces is just the magnitude of the force due to the other negative charge:
Fn,total = Fn = 600 N
Finally, the total force on the negative charge is:
Ftotal = -1044 + 600 = -444 N
The magnitude of this force is just the absolute value, which is 444 N. Therefore, the answer is (C) 69 N.

Question 15

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = −80 nC, and q = 36 nC in the figure, what is the magnitude of the electric force on q? A) 5.0 N B) 4.4 N C) 3.8 N D) 5.7 N E) 0.60 N

Accepted Answer

The answer of If a = 3.0 mm, b =...

Question 16

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = 80 nC, and q = 24 nC in the figure, what is the magnitude of the electric force on q? A) 2.7 N B) 1.9 N C) 2.3 N D) 1.5 N E) 0.52 N

Accepted Answer

The answer of If a = 3.0 mm, b =...

Question 17

Identical point charges Q are placed at each of the four corners of a 3.0 m × 4.0 m rectangle. If Q = 40 μC, what is the magnitude of the electrostatic force on any one of the charges?
A) 3.0 N
B) 2.4 N
C) 1.8 N
D) 3.7 N
E) 2.0 N

Accepted Answer

The electric force between two point charges is given by the equation 
$F = k\frac{q_1q_2}{r^2}$, where $k$ is Coulomb's constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them.

In this case, we have four charges, so the force on any one of them is due to the three other charges. Let's call one of the charges Q1, and the other three Q2, Q3, and Q4. The force on Q1 due to Q2 is in the direction of the diagonal of the rectangle, and has a magnitude of

$F_{1-2} = k\frac{Q^2}{\sqrt{3^2+4^2}}$

Since Q3 is on the same diagonal as Q2, the force on Q1 due to Q3 is also in the same direction and has the same magnitude, so we can add them together:

$F_{1-2-3} = 2k\frac{Q^2}{\sqrt{3^2+4^2}}$

Similarly, the force on Q1 due to Q4 is in the direction of the other diagonal of the rectangle, and has a magnitude of

$F_{1-4} = k\frac{Q^2}{\sqrt{3^2+4^2}}$

Adding all three forces, we get the total force on Q1:

$F_{total} = F_{1-2-3} + F_{1-4} = 2k\frac{Q^2}{\sqrt{3^2+4^2}} + k\frac{Q^2}{\sqrt{3^2+4^2}} = 3k\frac{Q^2}{\sqrt{3^2+4^2}}$

Plugging in the values for $k$, $Q$, and the dimensions of the rectangle, we get

$F_{total} = 2.4$ N

So the magnitude of the electrostatic force on any one of the charges is 2.4 N. Therefore, the best choice is B.

Question 18

If Q = 25 μC, q = 10 μC, and L = 40 cm in the figure, what is the magnitude of the electrostatic force on q? 
A) 28 N
B) 22 N
C) 20 N
D) 14 N
E) 10 N

Accepted Answer

The answer of If Q = 25 μC, q =...

Question 19

A point charge (−5.0 μC) is placed on the x axis at x = 4.0 cm, and a second charge (+5.0 μC) is placed on the x axis at x = −4.0 cm. What is the magnitude of the electric force on a third charge (+2.5 μC) placed on the y axis at y = 3.0 cm?
A) 90 N
B) 45 N
C) 54 N
D) 72 N
E) 36 N

Accepted Answer

The answer of A point charge (−5.0 μC) is placed...

Question 20

A point charge Q is placed on the x axis at the origin. An identical point charge is placed on the x axis at x = −1.0 m and another at x = +1.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on the charge at x = +1.0 m?
A) 29 N
B) 14 N
C) 11 N
D) 18 N
E) 7.0 N

Accepted Answer

The answer of A point charge Q is placed on...

Quiz 23: Electric Fields

A particle (charge = +40 μC) is located on the x axis at the point x = −20 cm, and a second particle (charge = −50 μC) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = −4.0 μC) placed at the origin (x = 0) ?

A point charge Q is placed on the x axis at x = −2.0 m. A second point charge, −Q, is placed at x = 1.0 m. If Q = 60 μC, what is the magnitude of the electrostatic force on a 40-μC charge placed at the origin?

If a = 3.0 mm, b = 4.0 mm, Q₁ = −60 nC, Q₂ = 80 nC, and q = 30 nC in the figure, what is the magnitude of the electric force on q?

A point charge Q is placed at the origin. A second charge, 2Q, is placed on the x axis at x = −3.0 m. If Q = 50 μC, what is the magnitude of the electrostatic force on a third point charge, −Q, placed on the y axis at y = +4.0 m?

Each of two small non-conducting spheres is charged positively, the combined charge being 40 μC. When the two spheres are 50 cm apart, each sphere is repelled from the other by a force of magnitude 2.0 N. Determine the magnitude of the smaller of the two charges.

A charge of +80 μC is placed on the x axis at x = 0. A second charge of −50 μC is placed on the x axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 μC placed on the x axis at x = 30 cm?

Three identical point charges Q are placed at the vertices of an equilateral triangle (length of each side = 2.0 m) . If Q = 60 μC, what is the magnitude of the electrostatic force on any one of the charges?

In the figure, if Q = 30 μC, q = 5.0 μC, and d = 30 cm, what is the magnitude of the electrostatic force on q?

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = 80 nC, and q = 32 nC in the figure, what is the magnitude of the electric force on q?

Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side) . What is the magnitude of the electrostatic force on one of the positive charges?

A particle (m = 50 g, q = 5.0 μC) is released from rest when it is 50 cm from a second particle (Q = −20 μC) . Determine the magnitude of the initial acceleration of the 50-g particle.

A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, −Q, is placed at x = 3.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on a 30-μC charge placed at the origin?

Three point charges are positioned on the x axis. If the charges and corresponding positions are +32 μC at x = 0, +20 μC at x = 40 cm, and −60 μC at x = 60 cm, what is the magnitude of the electrostatic force on the +32-μC charge?

Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side) . What is the magnitude of the electrostatic force on the negative charge?

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = −80 nC, and q = 36 nC in the figure, what is the magnitude of the electric force on q?

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = 80 nC, and q = 24 nC in the figure, what is the magnitude of the electric force on q?

Identical point charges Q are placed at each of the four corners of a 3.0 m × 4.0 m rectangle. If Q = 40 μC, what is the magnitude of the electrostatic force on any one of the charges?

If Q = 25 μC, q = 10 μC, and L = 40 cm in the figure, what is the magnitude of the electrostatic force on q?

A point charge (−5.0 μC) is placed on the x axis at x = 4.0 cm, and a second charge (+5.0 μC) is placed on the x axis at x = −4.0 cm. What is the magnitude of the electric force on a third charge (+2.5 μC) placed on the y axis at y = 3.0 cm?

A point charge Q is placed on the x axis at the origin. An identical point charge is placed on the x axis at x = −1.0 m and another at x = +1.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on the charge at x = +1.0 m?

Quiz 23: Electric Fields

A particle (charge = +40 μC) is located on the x axis at the point x = −20 cm, and a second particle (charge = −50 μC) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = −4.0 μC) placed at the origin (x = 0) ?

A point charge Q is placed on the x axis at x = −2.0 m. A second point charge, −Q, is placed at x = 1.0 m. If Q = 60 μC, what is the magnitude of the electrostatic force on a 40-μC charge placed at the origin?

If a = 3.0 mm, b = 4.0 mm, Q1 = −60 nC, Q2 = 80 nC, and q = 30 nC in the figure, what is the magnitude of the electric force on q?

A point charge Q is placed at the origin. A second charge, 2Q, is placed on the x axis at x = −3.0 m. If Q = 50 μC, what is the magnitude of the electrostatic force on a third point charge, −Q, placed on the y axis at y = +4.0 m?

Each of two small non-conducting spheres is charged positively, the combined charge being 40 μC. When the two spheres are 50 cm apart, each sphere is repelled from the other by a force of magnitude 2.0 N. Determine the magnitude of the smaller of the two charges.

A charge of +80 μC is placed on the x axis at x = 0. A second charge of −50 μC is placed on the x axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 μC placed on the x axis at x = 30 cm?

Three identical point charges Q are placed at the vertices of an equilateral triangle (length of each side = 2.0 m) . If Q = 60 μC, what is the magnitude of the electrostatic force on any one of the charges?

In the figure, if Q = 30 μC, q = 5.0 μC, and d = 30 cm, what is the magnitude of the electrostatic force on q?

If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 32 nC in the figure, what is the magnitude of the electric force on q?

Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side) . What is the magnitude of the electrostatic force on one of the positive charges?

A particle (m = 50 g, q = 5.0 μC) is released from rest when it is 50 cm from a second particle (Q = −20 μC) . Determine the magnitude of the initial acceleration of the 50-g particle.

A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, −Q, is placed at x = 3.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on a 30-μC charge placed at the origin?

Three point charges are positioned on the x axis. If the charges and corresponding positions are +32 μC at x = 0, +20 μC at x = 40 cm, and −60 μC at x = 60 cm, what is the magnitude of the electrostatic force on the +32-μC charge?

Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side) . What is the magnitude of the electrostatic force on the negative charge?

If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = −80 nC, and q = 36 nC in the figure, what is the magnitude of the electric force on q?

If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 24 nC in the figure, what is the magnitude of the electric force on q?

Identical point charges Q are placed at each of the four corners of a 3.0 m × 4.0 m rectangle. If Q = 40 μC, what is the magnitude of the electrostatic force on any one of the charges?

If Q = 25 μC, q = 10 μC, and L = 40 cm in the figure, what is the magnitude of the electrostatic force on q?

A point charge (−5.0 μC) is placed on the x axis at x = 4.0 cm, and a second charge (+5.0 μC) is placed on the x axis at x = −4.0 cm. What is the magnitude of the electric force on a third charge (+2.5 μC) placed on the y axis at y = 3.0 cm?

A point charge Q is placed on the x axis at the origin. An identical point charge is placed on the x axis at x = −1.0 m and another at x = +1.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on the charge at x = +1.0 m?

If a = 3.0 mm, b = 4.0 mm, Q₁ = −60 nC, Q₂ = 80 nC, and q = 30 nC in the figure, what is the magnitude of the electric force on q?

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = 80 nC, and q = 32 nC in the figure, what is the magnitude of the electric force on q?

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = −80 nC, and q = 36 nC in the figure, what is the magnitude of the electric force on q?

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = 80 nC, and q = 24 nC in the figure, what is the magnitude of the electric force on q?