Question 1

An alpha particle (charge = +2e) is sent at high speed toward a gold nucleus (charge +79e). What is the electrical force acting on the alpha particle when it is at a distance of 2 × 10⁻¹⁴ m away from the gold nucleus? (e = 1.6 × 10⁻¹⁹ C)

Accepted Answer

The answer of An alpha particle (charge = +2e) is...

Question 2

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the force on the knot at the center is ​  ​

Accepted Answer

The answer of Three 2.50-μC charges are placed on tiny...

Question 3

A charge of 50-μC is placed on the y axis at y = 3.0 cm and a 77-μC charge is placed on the x axis at x = 4.0 cm. If both charges are held fixed, what is the magnitude of the initial acceleration of an electron released from rest at the origin?

Accepted Answer

The correct answer is A because the initial acceleration of an electron released from rest at the origin is given by the equation a = (k * e) / m * (1 / r1^2 + 1 / r2^2), where k is Coulomb's constant, e is the charge of an electron, m is the mass of an electron, r1 is the distance from the electron to the first charge, and r2 is the distance from the electron to the second charge. Plugging in the given values, we get a = (9 * 10^9 N m^2 / C^2) * (1.6 * 10^-19 C) / (9.1 * 10^-31 kg) * (1 / (0.03 m)^2 + 1 / (0.04 m)^2) = 1.2 * 10^20 m/s^2.

Question 4

Two identical pith balls supported by insulating threads hang side by side and close together, as shown below.  One is positively charged; the other is neutral. We can conclude that

Accepted Answer

When two objects with different charges are close together, electric field lines will start at the positively charged object and terminate on the negatively charged object. In this case, the positively charged pith ball will have field lines leaving it and ending on the neutral pith ball next to it. However, not all the field lines will necessarily end on the neutral ball, as some may diverge and spread out into the surrounding space. Therefore, choice B is the best option as it accounts for both the transfer of field lines and the possibility of some field lines not ending on the neutral ball.

Question 5

Two charged particles, Q1 and Q2, are a distance r apart with Q2 = 5Q1. Compare the forces they exert on one another when  is the force Q2 exerts on Q1 and  is the force Q1 exerts on Q2.

Accepted Answer

The answer of Two charged particles, Q1 and Q2, are...

Question 6

Enrico says that positive charge is created when you rub a glass rod with silk, and that negative charge is simply the absence of positive charge. Rosetta says that negative charge is created and that positive charge is the absence of positive charge. (She has heard that Ben Franklin should have reversed the signs he associated with the charges.) Which one, if either, is correct?

Accepted Answer

When a glass rod is rubbed with silk, electrons (which carry negative charge) are transferred from one material to the other. This does not create charge but redistributes it, leaving one object positively charged (due to a deficit of electrons) and the other negatively charged (due to an excess of electrons). Both positive and negative charges are inherent in materials; the process of rubbing merely separates them.

Question 7

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the force on any one of the charges is ​  ​

Accepted Answer

The force between two charges can be calculated using Coulomb's law: 
$F=\frac{kq_1q_2}{r^2}$ where F is the force, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges. 
To find the net force on one of the charges, we need to calculate the force due to each of the other charges and then add them vectorially. 
Taking the direction of the force to be away from the other charges, the force due to one of the other charges is: 
$F_1=\frac{kq_1q_2}{r^2}$ where r is the distance between the two charges, which is given by the length of the string: r = 1 m. Substituting the given values, we get: 
$F_1=\frac{(9	imes 10^9 Nm^2/C^2)(2.50	imes 10^{-6} C)(2.50	imes 10^{-6} C)}{(1 m)^2}$
$F_1=562.50 N$
Since there are two other charges, with the same magnitude of charge, each of them will exert a force of 562.50 N on the given charge. These forces are acting at 120° angles to each other, so we can use the law of cosines to find the resultant force: 
$F_r^2=F_1^2+F_2^2-2F_1F_2\cos120^\circ$
$F_r^2=(562.50 N)^2+(562.50 N)^2-2(562.50 N)(562.50 N)\cos120^\circ$
$F_r^2= (562.50 N)^2+ (562.50 N)^2-2(562.50 N)^2(-0.5)$
$F_r^2= 2(562.50 N)^2(1+0.5)$
$F_r=(2.5981)(562.50 N)$
$F_r=1461.42 N$
Therefore, the magnitude of the net force on one of the charges is 1461.42 N, which is closest to answer choice B, 3.25 × 10^-11 N.

Question 8

Three pith balls supported by insulating threads hang from a support. We know that ball X is positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that

Accepted Answer

The answer of Three pith balls supported by insulating threads...

Question 9

Imagine for a minute that the Moon is held in its orbit about the Earth by electrical forces rather than by gravitation. What electrical charges −Q on the Earth and +Q on the Moon are necessary to hold the Moon in a circular orbit with a period of 27.3 days? The Earth-Moon distance is 384,000 km and the mass of the Moon is 7.35 × 10²² kg.

Accepted Answer

The answer of Imagine for a minute that the Moon...

Question 10

Rubber rods charged by rubbing with cat fur repel each other. Glass rods charged by rubbing with silk repel each other. A rubber rod and a glass rod charged respectively as above attract each other. A possible explanation is that

Accepted Answer

Rubber rods charged by rubbing with cat fur become negatively charged while glass rods charged by rubbing with silk become positively charged. Therefore, when a rubber rod and a glass rod are charged respectively as above, they have opposite charges and attract each other.

Question 11

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the tension in any one of the strings is ​  ​

Accepted Answer

The answer of Three 2.50-μC charges are placed on tiny...

Question 12

Three pith balls supported by insulating threads hang from a support. We know that ball X is positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that

Accepted Answer

Since ball X is positively charged, it will induce a separation of charges in balls Y and Z. Ball Y, which is attracted to ball X, must have a negative charge since opposite charges attract. Ball Z, which is repelled by ball X, must have a positive charge since like charges repel. Since pith is an insulating material, there is no way for charge to flow between the balls or the support, so the net charge on the system must be conserved. Therefore, ball Y is negatively charged or neutral (has no net charge).

Question 13

The symbol  appears in Coulomb's law because we use independently defined units for

Accepted Answer

The answer of The symbol  appears in Coulomb's law...

Question 14

Two tiny metal spheres are fixed to the ends of a non-conducting string of length  . Equal charges, +q, are placed on the metal spheres. Randall says that the force on the string has magnitude  . Tilden says that the tension in the string has magnitude  . Which one, if either, is correct?

Accepted Answer

Neither Randall nor Tilden is correct. The tension in the string can be found by analyzing the forces in the horizontal and vertical directions. The forces exerted by the charges on the string have components in both directions, so the tension will be greater than the magnitude of either force alone. 
Additionally, the net force on the string is zero because the forces exerted by the charges are equal and opposite. Therefore, the correct tension in the string is given by:
tension = 2Fsin(theta) = 2(kq^2/r)sin(theta) = 11eb8c7e_f59c_4864_8371_99bd695fe00e_TB8847_11.

Quiz 23: Electric Forces

An alpha particle (charge = +2e) is sent at high speed toward a gold nucleus (charge +79e). What is the electrical force acting on the alpha particle when it is at a distance of 2 × 10−14 m away from the gold nucleus? (e = 1.6 × 10−19 C)

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the force on the knot at the center is ​ ​

A charge of 50-μC is placed on the y axis at y = 3.0 cm and a 77-μC charge is placed on the x axis at x = 4.0 cm. If both charges are held fixed, what is the magnitude of the initial acceleration of an electron released from rest at the origin?

Two identical pith balls supported by insulating threads hang side by side and close together, as shown below. One is positively charged; the other is neutral. We can conclude that

Two charged particles, Q1 and Q2, are a distance r apart with Q2 = 5Q1. Compare the forces they exert on one another when is the force Q2 exerts on Q1 and is the force Q1 exerts on Q2.

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the force on any one of the charges is ​ ​

Three pith balls supported by insulating threads hang from a support. We know that ball X is positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that

Rubber rods charged by rubbing with cat fur repel each other. Glass rods charged by rubbing with silk repel each other. A rubber rod and a glass rod charged respectively as above attract each other. A possible explanation is that

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the tension in any one of the strings is ​ ​

Three pith balls supported by insulating threads hang from a support. We know that ball X is positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that

The symbol appears in Coulomb's law because we use independently defined units for

Two tiny metal spheres are fixed to the ends of a non-conducting string of length . Equal charges, +q, are placed on the metal spheres. Randall says that the force on the string has magnitude . Tilden says that the tension in the string has magnitude . Which one, if either, is correct?

An alpha particle (charge = +2e) is sent at high speed toward a gold nucleus (charge +79e). What is the electrical force acting on the alpha particle when it is at a distance of 2 × 10⁻¹⁴ m away from the gold nucleus? (e = 1.6 × 10⁻¹⁹ C)

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the force on the knot at the center is

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the force on any one of the charges is

Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the tension in any one of the strings is