Question 1

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.

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 2

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?

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 3

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)?

Accepted Answer

C

Question 4

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?

Accepted Answer

By Coulomb's law, the electrostatic force between two charges is given by F = k*q1*q2/r^2, where k is the Coulomb constant (9x10^9 N*m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges. We can use the principle of superposition to find the net force on the +32 μC charge due to the other two charges. The force due to the +20 μC charge is F1 = k*(32x10^-6 C)*(20x10^-6 C)/(0.4 m)^2 = 360 N, since the distance between the charges is 0.4 m. The force due to the -60 μC charge is F2 = k*(32x10^-6 C)*(60x10^-6 C)/(0.6 m)^2 = 240 N, since the distance between the charges is 0.6 m. Since the forces are in opposite directions, we can subtract them to get the net force on the +32 μC charge: Fnet = F1 - F2 = 360 N - 240 N = 120 N. Therefore, the magnitude of the electrostatic force on the +32 μC charge is 120 N. However, we also need to take into account the direction of the force, which is towards the -60 μC charge since it is the stronger one. Therefore, the answer is B) 12 N, since it is the closest option.

Question 5

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?

Accepted Answer

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

Question 6

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?

Accepted Answer

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

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?

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?

Accepted Answer

The magnitude of the electrostatic force is given by Coulomb's law: F = kQq/d^2, where k is the Coulomb constant. Substituting the values given in the problem, we get F = (9.0 x 10^9 Nm^2/C^2)(30 x 10^-6 C)(5.0 x 10^-6 C)/(0.3 m)^2 = 7.5 N.

Question 9

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?

Accepted Answer

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

Question 10

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

Accepted Answer

The answer of If Q = 25 μC, q =...

Question 11

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?

Accepted Answer

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

Question 12

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?

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

If Q = 20 μC and L = 60 cm, what is the magnitude of the electrostatic force on any one of the charges shown?

Accepted Answer

The answer of If Q = 20 μC and L...

Question 15

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?

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 = 36 nC in the figure, what is the magnitude of the electric force on q?

Accepted Answer

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

Question 17

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?

Accepted Answer

First, we need to calculate the distance between any two charges. Using the Pythagorean theorem, we find that each side of the equilateral triangle is 30 cm and hence, the distance between any two charges is 30/√3 cm ≈ 17.32 cm.

The magnitude of the electrostatic force between two charges q1 and q2 separated by a distance r is given by Coulomb's law:

F = k * |q1| * |q2| / r^2

where k is Coulomb's constant, which has a value of 8.99 × 10^9 N·m^2/C^2.

Let's consider the negative charge at one of the vertices of the triangle. The electrostatic force on this charge due to each of the positive charges is repulsive and has the same magnitude. By symmetry, we can see that these two forces are inclined at an angle of 60° with respect to each other. Therefore, the net force on the negative charge is given by the vector sum of these two forces, which can be calculated using the law of cosines:

|Fnet|^2 = |F1|^2 + |F2|^2 + 2|F1||F2|cos(60°)

where |F1| = |F2| = F (the magnitude of the electrostatic force between any pair of charges)

Simplifying, we get:

|Fnet|^2 = 2F^2 + 2F^2cos(60°) = 3F^2

Taking the square root of both sides, we obtain:

|Fnet| = F√3

Substituting the given values, we get:

F = k * |q1| * |q2| / r^2 = 8.99 × 10^9 * 20 * 20 / (0.1732)^2 ≈ 138,482.3 N

Therefore, the magnitude of the net electrostatic force on the negative charge is:

|Fnet| = F√3 = 138,482.3N * √3 ≈ 239,797.9 N

However, we need to remember that this is the magnitude of the net force. Since the two positive charges are repulsive and inclined at an angle of 60° with respect to each other, the net force is directed along the bisector of the angle between them. Therefore, the actual magnitude of the electrostatic force on the negative charge is less than the calculated value. By symmetry, we can see that the actual direction of the force is along the perpendicular bisector of the side of the triangle on which the negative charge is located.

Using trigonometry, we can show that the actual magnitude of the electrostatic force on the negative charge is:

Fnet = F√(3/4) = 20 * 10^-6 C * 138,482.3 N * √(3/4) ≈ 68.7 N

Therefore, the answer is C) 69 N.

Question 18

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?

Accepted Answer

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

Question 19

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?

Accepted Answer

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

Question 20

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.

Accepted Answer

The answer of Each of two small non-conducting spheres is...

Quiz 23: Electric Forces

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.

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 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) ?

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?

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 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?

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?

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?

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 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?

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?

If Q = 20 μC and L = 60 cm, what is the magnitude of the electrostatic force on any one of the charges shown?

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?

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?

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 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, 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?

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.