Question 1

Five equal negative charges are uniformly spaced in a semicircular arc of radius r₀ with its center at the origin.The charges positions in polar coordinates are given by (r₀,θ_i),where the values of θ_iare 0°,45°,90°,135°,and 180°.At the position (x,y)= (r₀,-r₀)in the 4th quadrant,which statement best describes the direction of the resulting electric field?

Accepted Answer

The electric field at the point (r, -r) due to the five charges will have components in both the x and y directions. The x-component of the electric field will be zero due to the symmetry of the charges, while the y-component will be the sum of the y-components of the individual electric fields due to each charge. 
Since the charges are equally spaced in a semicircular arc, the y-components of the electric fields due to the charges at 0° and 180° will cancel each other out, as will the y-components of the electric fields due to the charges at 45° and 135°. The only remaining y-component will be from the charge at 90°, which will point downwards in the negative y-direction. 
Thus, the resulting electric field at the point (r, -r) will be in the 4th quadrant, with a direction of a 2nd quadrant angle (i.e. downwards and to the right). Therefore, the correct answer is choice D.

Question 2

An electron is sent at high speed toward a gold nucleus (charge +79e).What is the electrical force acting on the electron when it is 1.7 × 10−¹⁴ m away from the gold nucleus? (e = 1.6 × 10−¹⁹ C,k_e = 8.99 × 10⁹ N·m²/C²)

Accepted Answer

The electrical force can be calculated using Coulomb's law: F = k_e * |q1 * q2| / r^2. Substituting the given values: F = (8.99 × 10^9 N·m^2/C^2) * |(-1.6 × 10^-19 C) * (79 * 1.6 × 10^-19 C)| / (1.7 × 10^-14 m)^2 = 6.3E+1 N.

Question 3

A 6.6-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.1 m.If the resulting force on the second charge is 5.7 N in the positive x-direction,what is the value of its charge?​

Accepted Answer

The force between two charges is given by Coulomb's law, $F = k \frac{|q_1 q_2|}{r^2}$, where $k = 8.987 \times 10^9 \, \text{N m}^2/\text{C}^2$, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them. Given $F = 5.7 \, \text{N}$, $q_1 = 6.6 \, \mu\text{C} = 6.6 \times 10^{-6} \, \text{C}$, and $r = 0.1 \, \text{m}$, we can solve for $q_2$. The direction of the force indicates that $q_2$ has the same sign as $q_1$, making it positive. Solving for $q_2$ gives a value close to $1.0 \, \mu\text{C}$, indicating that the charges repel each other, consistent with them having the same sign.

Question 4

An electron with a charge value of 1.6 × 10−¹⁹ C is moving in the presence of an electric field of 400 N/C.What force does the electron experience?

Accepted Answer

The force experienced by an electron in an electric field is calculated using the formula F = qE, where q is the charge of the electron (1.6 × 10^-19 C) and E is the electric field strength (400 N/C). Thus, F = (1.6 × 10^-19 C) * (400 N/C) = 6.4 × 10^-17 N.

Question 5

The electric field of a point charge has an inverse ________ behavior.

Accepted Answer

The electric field of a point charge follows an inverse square law, meaning it decreases in strength as the square of the distance from the charge, which is represented by $r^{-2}$.

Question 6

Two point charges each have a value of 35.5 mC and are separated by a distance of 4.0 cm.What is the electric field midway between the two charges? (k_e = 8.99 × 10⁹ N·m²/C²)

Accepted Answer

The electric field midway between two like charges is zero because the fields due to each charge at that point are equal in magnitude but opposite in direction, thus canceling each other out.

Question 7

Charge A and charge B are 3.00 m apart,and charge A is +1.44 C and charge B is +3.10 C.Charge C is located between them at a certain point and the force on charge C is zero.How far from charge A is charge C?​

Accepted Answer

The answer of Charge A and charge B are 3.00...

Question 8

If the size of the charge value is tripled for both of two point charges maintained at a constant separation,the mutual force between them will be changed by what factor?

Accepted Answer

The mutual force between two charges is directly proportional to the product of their charges, so if both charges are tripled, the product of their charges will be 9 times greater. Therefore, the mutual force between them will also be 9 times greater.

Question 9

Two equal charges,each Q,are separated by some distance.What third charge would need to be placed half way between the two charges so that the net force on each charge would be zero?

Accepted Answer

The answer of Two equal charges,each Q,are separated by some...

Question 10

A 7.0-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.3 m.If the resulting force on the second charge is 6.9 N in the positive x-direction,what is the force on the charge at the origin?​

Accepted Answer

According to Newton's third law, for every action, there is an equal and opposite reaction. Therefore, if the second charge experiences a force of 6.9 N in the positive x-direction due to the first charge, the first charge must experience an equal force of 6.9 N in the opposite direction, which is the negative x-direction.

Question 11

​A charged particle with mass m is suspended in the air by an upward-directed electric field E.What is the charge on the dust particle?

Accepted Answer

For a charged particle to be suspended in the air by an electric field, the electric force (qE) must balance the gravitational force (mg). Thus, qE = mg. Solving for q gives q = mg/E.

Question 12

Two point charges,one q and the other -q,form a dipole separated by a distance 2L.A third charge Q is placed midway between these two charges.If the only charge that is negative is -q,what is the force on Q?

Accepted Answer

The answer of Two point charges,one q and the other...

Question 13

If the distance between two point charges is doubled,the mutual force between them will be changed by what factor?

Accepted Answer

According to the inverse square law of electrostatics, the force between two point charges is inversely proportional to the square of the distance between them. Therefore, if the distance is doubled, the force will be reduced to 1/4th of its original value. Hence, the answer is D, i.e., 1/4.

Question 14

Four charges are at the corners of a square,with B and C on opposite 
Corners.Charges A and D,on the other two corners,have equal charge,while both B and C have a charge of +1.0 C.What is the charge on A so that the force on B is zero?

Accepted Answer

The answer of Four charges are at the corners of...

Question 15

Electric field is dimensionally equivalent to which of the following?

Accepted Answer

The electric field is defined as the force per unit charge, which gives it the dimension of N/C (newtons per coulomb).

Question 16

Two electrons are separated by 7.0 cm.What is the ratio of the electric force to the gravitational force between them? (m_e = 9.11 × 10−³¹ kg,k_e = 8.99 × 10⁹ N⋅m²/C²,G = 6.67 × 10^-11 N⋅m²/kg²,and e = 1.6 × 10−¹⁹ C)

Accepted Answer

The electric force between two electrons is calculated using Coulomb's law, and the gravitational force is calculated using Newton's law of universal gravitation. The ratio of these forces is extremely large due to the much stronger electric force compared to the gravitational force at the atomic scale.

Question 17

Two point charges are 12 cm apart.They are moved to a new separation of 3 cm.By what factor does the resulting mutual force between them change?

Accepted Answer

The force between two charges is given by Coulomb's law: F = k(q1q2)/r^2. 
When the separation distance is decreased from 12 cm to 3 cm, the denominator of the formula decreases by a factor of (12/3)^2 = 16. 
Thus, the force between the charges increases by a factor of 16. 
Therefore, the correct answer is D) 16.

Question 18

The constant k_e,which appears in Coulomb's law formula,is equivalent dimensionally to which of the following?

Accepted Answer

The constant $k$ in Coulomb's law, which is dimensionally equivalent to $N \cdot m^2 / C^2$, is represented in the question as $N \cdot m^{²} / C^{²}$, where the superscript notation $²$ likely indicates squared units, thus matching the dimensional formula for $k$.

Question 19

Two point charges are separated by 12.0 cm and have charges of +5.0 µC and −5.0 µC,respectively.What is the electric field at a point midway between the two charges? (k_e = 8.99 × 10⁹ N·m²/C²)

Accepted Answer

The electric field due to each charge at the midpoint is equal in magnitude but opposite in direction. The fields add up because they are in the same direction (towards the negative charge). The magnitude of the electric field due to one charge is E = k * |q| / (r^2), where r = 0.06 m. Calculating gives E = 2.5 × 10^7 N/C.

Question 20

In a thundercloud there may be an electric charge of +30 C near the top of the cloud and −30 C near the bottom of the cloud.These charges are separated by about 4.00 km.What is the electric force between these two sets of charges? (k_e = 8.99 × 10⁹ N·m²/C²)

Accepted Answer

The answer of In a thundercloud there may be an...

Quiz 15: Electric Forces and Fields

An electron is sent at high speed toward a gold nucleus (charge +79e) .What is the electrical force acting on the electron when it is 1.7 × 10−¹⁴ m away from the gold nucleus? (e = 1.6 × 10−¹⁹ C,k_e = 8.99 × 10⁹ N·m²/C²)

A 6.6-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.1 m.If the resulting force on the second charge is 5.7 N in the positive x-direction,what is the value of its charge?

An electron with a charge value of 1.6 × 10−¹⁹ C is moving in the presence of an electric field of 400 N/C.What force does the electron experience?

The electric field of a point charge has an inverse ________ behavior.

Two point charges each have a value of 35.5 mC and are separated by a distance of 4.0 cm.What is the electric field midway between the two charges? (k_e = 8.99 × 10⁹ N·m²/C²)

Charge A and charge B are 3.00 m apart,and charge A is +1.44 C and charge B is +3.10 C.Charge C is located between them at a certain point and the force on charge C is zero.How far from charge A is charge C?

If the size of the charge value is tripled for both of two point charges maintained at a constant separation,the mutual force between them will be changed by what factor?

Two equal charges,each Q,are separated by some distance.What third charge would need to be placed half way between the two charges so that the net force on each charge would be zero?

A 7.0-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.3 m.If the resulting force on the second charge is 6.9 N in the positive x-direction,what is the force on the charge at the origin?

A charged particle with mass m is suspended in the air by an upward-directed electric field E.What is the charge on the dust particle?

Two point charges,one q and the other -q,form a dipole separated by a distance 2L.A third charge Q is placed midway between these two charges.If the only charge that is negative is -q,what is the force on Q?

If the distance between two point charges is doubled,the mutual force between them will be changed by what factor?

Four charges are at the corners of a square,with B and C on opposite Corners.Charges A and D,on the other two corners,have equal charge,while both B and C have a charge of +1.0 C.What is the charge on A so that the force on B is zero?

Electric field is dimensionally equivalent to which of the following?

Two electrons are separated by 7.0 cm.What is the ratio of the electric force to the gravitational force between them? (m_e = 9.11 × 10−³¹ kg,k_e = 8.99 × 10⁹ N⋅m²/C²,G = 6.67 × 10^-11 N⋅m²/kg²,and e = 1.6 × 10−¹⁹ C)

Two point charges are 12 cm apart.They are moved to a new separation of 3 cm.By what factor does the resulting mutual force between them change?

The constant k_e,which appears in Coulomb's law formula,is equivalent dimensionally to which of the following?

Two point charges are separated by 12.0 cm and have charges of +5.0 µC and −5.0 µC,respectively.What is the electric field at a point midway between the two charges? (k_e = 8.99 × 10⁹ N·m²/C²)

In a thundercloud there may be an electric charge of +30 C near the top of the cloud and −30 C near the bottom of the cloud.These charges are separated by about 4.00 km.What is the electric force between these two sets of charges? (k_e = 8.99 × 10⁹ N·m²/C²)

Quiz 15: Electric Forces and Fields

An electron is sent at high speed toward a gold nucleus (charge +79e) .What is the electrical force acting on the electron when it is 1.7 × 10−14 m away from the gold nucleus? (e = 1.6 × 10−19 C,ke = 8.99 × 109 N·m2/C2) ​

A 6.6-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.1 m.If the resulting force on the second charge is 5.7 N in the positive x-direction,what is the value of its charge?​

An electron with a charge value of 1.6 × 10−19 C is moving in the presence of an electric field of 400 N/C.What force does the electron experience?

The electric field of a point charge has an inverse ________ behavior.

Two point charges each have a value of 35.5 mC and are separated by a distance of 4.0 cm.What is the electric field midway between the two charges? (ke = 8.99 × 109 N·m2/C2) ​

Charge A and charge B are 3.00 m apart,and charge A is +1.44 C and charge B is +3.10 C.Charge C is located between them at a certain point and the force on charge C is zero.How far from charge A is charge C?​

If the size of the charge value is tripled for both of two point charges maintained at a constant separation,the mutual force between them will be changed by what factor?

Two equal charges,each Q,are separated by some distance.What third charge would need to be placed half way between the two charges so that the net force on each charge would be zero?

A 7.0-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.3 m.If the resulting force on the second charge is 6.9 N in the positive x-direction,what is the force on the charge at the origin?​

​A charged particle with mass m is suspended in the air by an upward-directed electric field E.What is the charge on the dust particle?

Two point charges,one q and the other -q,form a dipole separated by a distance 2L.A third charge Q is placed midway between these two charges.If the only charge that is negative is -q,what is the force on Q?

If the distance between two point charges is doubled,the mutual force between them will be changed by what factor?

Four charges are at the corners of a square,with B and C on opposite Corners.Charges A and D,on the other two corners,have equal charge,while both B and C have a charge of +1.0 C.What is the charge on A so that the force on B is zero?

Electric field is dimensionally equivalent to which of the following?

Two electrons are separated by 7.0 cm.What is the ratio of the electric force to the gravitational force between them? (me = 9.11 × 10−31 kg,ke = 8.99 × 109 N⋅m2/C2,G = 6.67 × 10-11 N⋅m2/kg2,and e = 1.6 × 10−19 C) ​

Two point charges are 12 cm apart.They are moved to a new separation of 3 cm.By what factor does the resulting mutual force between them change?

The constant ke,which appears in Coulomb's law formula,is equivalent dimensionally to which of the following?

Two point charges are separated by 12.0 cm and have charges of +5.0 µC and −5.0 µC,respectively.What is the electric field at a point midway between the two charges? (ke = 8.99 × 109 N·m2/C2)

In a thundercloud there may be an electric charge of +30 C near the top of the cloud and −30 C near the bottom of the cloud.These charges are separated by about 4.00 km.What is the electric force between these two sets of charges? (ke = 8.99 × 109 N·m2/C2) ​

An electron is sent at high speed toward a gold nucleus (charge +79e) .What is the electrical force acting on the electron when it is 1.7 × 10−¹⁴ m away from the gold nucleus? (e = 1.6 × 10−¹⁹ C,k_e = 8.99 × 10⁹ N·m²/C²)

A 6.6-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.1 m.If the resulting force on the second charge is 5.7 N in the positive x-direction,what is the value of its charge?

An electron with a charge value of 1.6 × 10−¹⁹ C is moving in the presence of an electric field of 400 N/C.What force does the electron experience?

Two point charges each have a value of 35.5 mC and are separated by a distance of 4.0 cm.What is the electric field midway between the two charges? (k_e = 8.99 × 10⁹ N·m²/C²)

Charge A and charge B are 3.00 m apart,and charge A is +1.44 C and charge B is +3.10 C.Charge C is located between them at a certain point and the force on charge C is zero.How far from charge A is charge C?

A 7.0-μC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.3 m.If the resulting force on the second charge is 6.9 N in the positive x-direction,what is the force on the charge at the origin?

A charged particle with mass m is suspended in the air by an upward-directed electric field E.What is the charge on the dust particle?

Two electrons are separated by 7.0 cm.What is the ratio of the electric force to the gravitational force between them? (m_e = 9.11 × 10−³¹ kg,k_e = 8.99 × 10⁹ N⋅m²/C²,G = 6.67 × 10^-11 N⋅m²/kg²,and e = 1.6 × 10−¹⁹ C)

The constant k_e,which appears in Coulomb's law formula,is equivalent dimensionally to which of the following?

Two point charges are separated by 12.0 cm and have charges of +5.0 µC and −5.0 µC,respectively.What is the electric field at a point midway between the two charges? (k_e = 8.99 × 10⁹ N·m²/C²)

In a thundercloud there may be an electric charge of +30 C near the top of the cloud and −30 C near the bottom of the cloud.These charges are separated by about 4.00 km.What is the electric force between these two sets of charges? (k_e = 8.99 × 10⁹ N·m²/C²)