Question 1

In a thundercloud there may be an electric charge of +40 C near the top of the cloud and -40 C near the bottom of the cloud.These charges are separated by about 2.0 km.What is the electric force between these two sets of charges? (k_e = 8.99 x 10⁹ N·m²/C²)

Accepted Answer

The electric force can be calculated using Coulomb's law: F = k_e * |q1 * q2| / r^2. Substituting the given values: F = (8.99 x 10^9 N·m^2/C^2) * (40 C * 40 C) / (2000 m)^2 = 3.6 x 10^6 N.

Question 2

An electron with a charge value of 1.6 x 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 a charge in an electric field is given by F = qE, where q is the charge and E is the electric field. Substituting the given values, F = (1.6 x 10^-19 C)(400 N/C) = 6.4 x 10^-17 N.

Question 3

The average distance of the electron from the proton in the hydrogen atom is 0.51 x 10^-10 m.What is the electric field from the proton's charge at the location of the electron? (k_e = 8.99 x 10⁹ N*m²/C²,e = 1.6 x 10^-19 C)

Accepted Answer

The electric field E due to a point charge is given by E = k_e * |q| / r^2. Substituting the given values: E = (8.99 x 10^9 N m^2/C^2) * (1.6 x 10^-19 C) / (0.51 x 10^-10 m)^2 = 5.5 x 10^11 N/C.

Question 4

Two point charges each have a value of 30.0 mC and are separated by a distance of 4.00 cm.What is the electric field midway between the two charges? (k_e = 8.99 x 10⁹ N·m²/C²)

Accepted Answer

Since the two charges have the same magnitude and are equidistant from the midpoint, they will create electric fields with equal magnitudes that point in opposite directions. Therefore, the net electric field at the midpoint will be zero.

Question 5

A charge of +2 C is at the origin.When charge Q is placed at 2 m along the positive x axis,the electric field at 2 m along the negative x axis becomes zero.What is the value of Q?

Accepted Answer

The answer of A charge of +2 C is at...

Question 6

Charges of 4.0 µC and -6.0 µC are placed at two corners of an equilateral triangle with sides of 0.10 m.At the third corner,what is the electric field magnitude created by these two charges? (k_e = 8.99 x 10⁹ N·m²/C²)

Accepted Answer

The answer of Charges of 4.0 µC and -6.0 µC...

Question 7

A 6.00 mC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.300 m.If the resulting force on the second charge is 6.40 N in the positive x-direction,what is the force on the charge at the origin?

Accepted Answer

The force on the charge at the origin is equal in magnitude but opposite in direction to the force on the second charge. This is due to the fact that the force between two charges is always equal and opposite. Therefore, the force on the charge at the origin is 6.40 N in the negative x-direction.

Question 8

A proton initially moves left to right long the x axis at a speed of 2.00 x 10³m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.200 m before coming to rest.If the proton's mass and charge are 1.67 x 10^-27kg and 1.60 x 10^-19C respectively,what is the magnitude of the electric field?

Accepted Answer

We can use the formula for the work done by an electric field on a charged particle to solve for the magnitude of the electric field:

W = qEd

where W is the work done, q is the charge of the particle, E is the electric field strength, and d is the distance traveled in the electric field.

Since the proton comes to rest, all of its initial kinetic energy is converted into potential energy due to the electric field:

KEi = PEf

(1/2)mv^2 = qEd

We can solve for E:

E = (1/2)mv^2 / qd

Plugging in the given values:

E = (1/2)(1.67 x 10^-27 kg)(2.00 x 10^13 m/s)^2 / (1.60 x 10^-19 C)(0.200 m)

E = 0.104 N/C

Therefore, the correct answer is (C).

Question 9

The beam of electrons that hits the screen of an oscilloscope is moved up and down by:

Accepted Answer

The beam of electrons is moved up and down by electrical charges on deflecting plates. The phosphorescent coating on the screen only serves to emit light when struck by the electrons, and varying the electron's charge would not affect the position of the beam on the screen. Gravity has no effect on the movement of the beam.

Question 10

A proton initially moves left to right long the x axis at a speed of 2.00 x 10³ m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.200 m before coming to rest.What acceleration magnitude does the proton experience?

Accepted Answer

The acceleration can be found using the kinematic equation: $ v^2 = u^2 + 2as $. Here, $ v = 0 $, $ u = 2.00 \times 10^3 \, \text{m/s} $, and $ s = 0.200 \, \text{m} $. Solving for $ a $, we get $ a = \frac{-u^2}{2s} = \frac{-(2.00 \times 10^3)^2}{2 \times 0.200} = 1.00 \times 10^7 \, \text{m/s}^2 $.

Question 11

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 3.0 x 10^-14 m away from the gold nucleus? (e = 1.6 x 10^-19 C,k_e = 8.99 x 10⁹ N·m²/C²)

Accepted Answer

The answer of An electron is sent at high speed...

Question 12

Two point charges are placed along a horizontal axis with the following values and positions: +3.0 µC at x = 0 cm and -7.0 µC at x = 20 cm.At what point along the x axis is the electric field zero?

Accepted Answer

The answer of Two point charges are placed along a...

Question 13

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

By symmetry, we know that the third charge must be equidistant from the two original charges. Therefore, it forms an equilateral triangle between the two original charges. Let's label the third charge as q.

From the principle of superposition, we know that the net force on each of the original charges is equal to the sum of the forces from the other two charges. Suppose the distance between the two original charges is d. The force between them is kQ^2/d^2, where k is Coulomb's constant.

By symmetry, the two forces acting on the third charge must cancel out. This means that the magnitudes of the two forces must be equal, and they must be directed towards the third charge.

Let's call the distance between each of the original charges and the third charge x. We can use the Pythagorean theorem to relate x and d:

x^2 + (d/2)^2 = (d/2)^2

Simplifying, we get x = d/2√3. Now we can calculate the force on each of the original charges due to the third charge q:

F = kQq/x^2 = kQq/[(d/2√3)^2]

Since the two forces on the original charges cancel out, we can set them equal to each other and solve for q:

kQ^2/d^2 = 2F = 2(kQq)/[(d/2√3)^2]

Simplifying, we get q = Q/4. Therefore, the answer is (C) -Q/4.

Question 14

An electron with a speed of 2.0 x 10⁶ m/s moves into a uniform electric field of 500 N/C that is parallel to the electron's motion.How long does it take to bring the electron to rest? (m_e= 9.11 x 10^-31 kg,e = 1.6 x 10^-19 C)

Accepted Answer

The force on the electron is F = eE = 1.6 x 10^-19 C * 500 N/C = 8 x 10^-17 N. The acceleration is a = F/m = 8 x 10^-17 N / 9.11 x 10^-31 kg = 8.78 x 10^13 m/s^2. The time to stop is t = v/a = (2.0 x 10^6 m/s) / (8.78 x 10^13 m/s^2) = 2.3 x 10^-8 s.

Question 15

Electric field is dimensionally equivalent to which of the following?

Accepted Answer

The unit of electric field is Newton per Coulomb (N/C), and option B represents the same dimensionally. All other options have additional and unnecessary units that do not match the dimension of electric field.

Question 16

Two charges,+Q and -Q,are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated.Which vector best represents the direction of the electric field at that point?

Accepted Answer

The answer of Two charges,+Q and -Q,are located two meters...

Question 17

Two electrons are separated by one cm.What is the ratio of the electric force to the gravitational force between them? (m_e = 9.11 x 10^-31kg,k_e = 8.99 x 10⁹ N*m²/C²,G = 6.67 x 10^-11 N*m²/kg²,and e = 1.6 x 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 because the electric force is much stronger than the gravitational force at the atomic scale.

Question 18

In x-ray machines,electrons are subjected to electric fields as great as 6.0 x 10⁵ N/C.Find an electron's acceleration in this field.(m_e = 9.11 x 10^-31 kg,e = 1.6 x 10^-19 C)

Accepted Answer

The acceleration can be calculated using the formula $ a = \frac{F}{m} $, where $ F = eE $. Substituting the given values, $ a = \frac{(1.6 \times 10^{-19} \, \text{C})(6.0 \times 10^5 \, \text{N/C})}{9.11 \times 10^{-31} \, \text{kg}} = 1.1 \times 10^{17} \, \text{m/s}^2 $.

Question 19

A 6.0 mC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.30 m.If the resulting force on the second charge is 5.4 N in the positive x-direction,what is the value of its charge?

Accepted Answer

The force on the second charge is given by Coulomb's law:$$F = k\frac{q_1q_2}{r^2}$$where k is Coulomb's constant, q1 is the charge at the origin, q2 is the charge on the x-axis, and r is the distance between the charges.We are given that F = 5.4 N, q1 = 6.0 mC, r = 0.30 m, and we want to find q2.Substituting these values into Coulomb's law, we get:$$5.4 N = (9.0 	imes 10^9 Nm^2/C^2)\frac{(6.0 	imes 10^{-3} C)q_2}{(0.30 m)^2}$$Solving for q2, we get:$$q_2 = 9.0 	imes 10^{-3} C = 9.0 mC$$Therefore, the charge on the x-axis is 9.0 mC.

Question 20

Two point charges are separated by 10.0 cm and have charges of +2.00 µC and -2.00 µC,respectively.What is the electric field at a point midway between the two charges? (k_e = 8.99 x 10⁹ N·m²/C²)

Accepted Answer

Using the formula for electric field due to a point charge: 
E = (k|Q|)/r^2 
where k is Coulomb's constant, Q is the charge and r is the distance from the point charge.

At the midpoint, the distance from each charge is 5 cm. Therefore, the electric field due to each charge is:

E1 = (8.99 × 10^9 N·m^2/C^2) × (2.00 × 10^-6 C) / (0.05 m)^2 = 7.19 × 10^4 N/C 
E2 = (8.99 × 10^9 N·m^2/C^2) × (2.00 × 10^-6 C) / (0.05 m)^2 = 7.19 × 10^4 N/C

The electric fields are in opposite directions, so we must subtract to find the net electric field:

E = E1 - E2 = 0

Therefore, the electric field at the midpoint is zero. The correct choice is B.

Quiz 15: Electric Forces and Electric Fields

In a thundercloud there may be an electric charge of +40 C near the top of the cloud and -40 C near the bottom of the cloud.These charges are separated by about 2.0 km.What is the electric force between these two sets of charges? (k_e = 8.99 x 10⁹ N·m²/C²)

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

The average distance of the electron from the proton in the hydrogen atom is 0.51 x 10^-10 m.What is the electric field from the proton's charge at the location of the electron? (k_e = 8.99 x 10⁹ N*m²/C²,e = 1.6 x 10^-19 C)

Two point charges each have a value of 30.0 mC and are separated by a distance of 4.00 cm.What is the electric field midway between the two charges? (k_e = 8.99 x 10⁹ N·m²/C²)

A charge of +2 C is at the origin.When charge Q is placed at 2 m along the positive x axis,the electric field at 2 m along the negative x axis becomes zero.What is the value of Q?

Charges of 4.0 µC and -6.0 µC are placed at two corners of an equilateral triangle with sides of 0.10 m.At the third corner,what is the electric field magnitude created by these two charges? (k_e = 8.99 x 10⁹ N·m²/C²)

A 6.00 mC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.300 m.If the resulting force on the second charge is 6.40 N in the positive x-direction,what is the force on the charge at the origin?

The beam of electrons that hits the screen of an oscilloscope is moved up and down by:

A proton initially moves left to right long the x axis at a speed of 2.00 x 10³ m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.200 m before coming to rest.What acceleration magnitude does the proton experience?

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 3.0 x 10^-14 m away from the gold nucleus? (e = 1.6 x 10^-19 C,k_e = 8.99 x 10⁹ N·m²/C²)

Two point charges are placed along a horizontal axis with the following values and positions: +3.0 µC at x = 0 cm and -7.0 µC at x = 20 cm.At what point along the x axis is the electric field zero?

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?

An electron with a speed of 2.0 x 10⁶ m/s moves into a uniform electric field of 500 N/C that is parallel to the electron's motion.How long does it take to bring the electron to rest? (m_e= 9.11 x 10^-31 kg,e = 1.6 x 10^-19 C)

Electric field is dimensionally equivalent to which of the following?

Two charges,+Q and -Q,are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated.Which vector best represents the direction of the electric field at that point?

Two electrons are separated by one cm.What is the ratio of the electric force to the gravitational force between them? (m_e = 9.11 x 10^-31kg,k_e = 8.99 x 10⁹ Nm²/C²,G = 6.67 x 10^-11 Nm²/kg²,and e = 1.6 x 10^-19 C)

In x-ray machines,electrons are subjected to electric fields as great as 6.0 x 10⁵ N/C.Find an electron's acceleration in this field.(m_e = 9.11 x 10^-31 kg,e = 1.6 x 10^-19 C)

A 6.0 mC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.30 m.If the resulting force on the second charge is 5.4 N in the positive x-direction,what is the value of its charge?

Two point charges are separated by 10.0 cm and have charges of +2.00 µC and -2.00 µC,respectively.What is the electric field at a point midway between the two charges? (k_e = 8.99 x 10⁹ N·m²/C²)

Quiz 15: Electric Forces and Electric Fields

In a thundercloud there may be an electric charge of +40 C near the top of the cloud and -40 C near the bottom of the cloud.These charges are separated by about 2.0 km.What is the electric force between these two sets of charges? (ke = 8.99 x 109 N·m2/C2)

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

The average distance of the electron from the proton in the hydrogen atom is 0.51 x 10-10 m.What is the electric field from the proton's charge at the location of the electron? (ke = 8.99 x 109 N*m2/C2,e = 1.6 x 10-19 C)

Two point charges each have a value of 30.0 mC and are separated by a distance of 4.00 cm.What is the electric field midway between the two charges? (ke = 8.99 x 109 N·m2/C2)

A charge of +2 C is at the origin.When charge Q is placed at 2 m along the positive x axis,the electric field at 2 m along the negative x axis becomes zero.What is the value of Q?

Charges of 4.0 µC and -6.0 µC are placed at two corners of an equilateral triangle with sides of 0.10 m.At the third corner,what is the electric field magnitude created by these two charges? (ke = 8.99 x 109 N·m2/C2)

A 6.00 mC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.300 m.If the resulting force on the second charge is 6.40 N in the positive x-direction,what is the force on the charge at the origin?

The beam of electrons that hits the screen of an oscilloscope is moved up and down by:

A proton initially moves left to right long the x axis at a speed of 2.00 x 103 m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.200 m before coming to rest.What acceleration magnitude does the proton experience?

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 3.0 x 10-14 m away from the gold nucleus? (e = 1.6 x 10-19 C,ke = 8.99 x 109 N·m2/C2)

Two point charges are placed along a horizontal axis with the following values and positions: +3.0 µC at x = 0 cm and -7.0 µC at x = 20 cm.At what point along the x axis is the electric field zero?

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?

An electron with a speed of 2.0 x 106 m/s moves into a uniform electric field of 500 N/C that is parallel to the electron's motion.How long does it take to bring the electron to rest? (me = 9.11 x 10-31 kg,e = 1.6 x 10-19 C)

Electric field is dimensionally equivalent to which of the following?

Two charges,+Q and -Q,are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated.Which vector best represents the direction of the electric field at that point?

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

In x-ray machines,electrons are subjected to electric fields as great as 6.0 x 105 N/C.Find an electron's acceleration in this field.(me = 9.11 x 10-31 kg,e = 1.6 x 10-19 C)

A 6.0 mC charge is placed at the origin and a second charge is placed on the x-axis at x = 0.30 m.If the resulting force on the second charge is 5.4 N in the positive x-direction,what is the value of its charge?

Two point charges are separated by 10.0 cm and have charges of +2.00 µC and -2.00 µC,respectively.What is the electric field at a point midway between the two charges? (ke = 8.99 x 109 N·m2/C2)

In a thundercloud there may be an electric charge of +40 C near the top of the cloud and -40 C near the bottom of the cloud.These charges are separated by about 2.0 km.What is the electric force between these two sets of charges? (k_e = 8.99 x 10⁹ N·m²/C²)

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

The average distance of the electron from the proton in the hydrogen atom is 0.51 x 10^-10 m.What is the electric field from the proton's charge at the location of the electron? (k_e = 8.99 x 10⁹ N*m²/C²,e = 1.6 x 10^-19 C)

Two point charges each have a value of 30.0 mC and are separated by a distance of 4.00 cm.What is the electric field midway between the two charges? (k_e = 8.99 x 10⁹ N·m²/C²)

Charges of 4.0 µC and -6.0 µC are placed at two corners of an equilateral triangle with sides of 0.10 m.At the third corner,what is the electric field magnitude created by these two charges? (k_e = 8.99 x 10⁹ N·m²/C²)

A proton initially moves left to right long the x axis at a speed of 2.00 x 10³ m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.200 m before coming to rest.What acceleration magnitude does the proton experience?

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 3.0 x 10^-14 m away from the gold nucleus? (e = 1.6 x 10^-19 C,k_e = 8.99 x 10⁹ N·m²/C²)

An electron with a speed of 2.0 x 10⁶ m/s moves into a uniform electric field of 500 N/C that is parallel to the electron's motion.How long does it take to bring the electron to rest? (m_e= 9.11 x 10^-31 kg,e = 1.6 x 10^-19 C)

Two electrons are separated by one cm.What is the ratio of the electric force to the gravitational force between them? (m_e = 9.11 x 10^-31kg,k_e = 8.99 x 10⁹ Nm²/C²,G = 6.67 x 10^-11 Nm²/kg²,and e = 1.6 x 10^-19 C)

In x-ray machines,electrons are subjected to electric fields as great as 6.0 x 10⁵ N/C.Find an electron's acceleration in this field.(m_e = 9.11 x 10^-31 kg,e = 1.6 x 10^-19 C)

Two point charges are separated by 10.0 cm and have charges of +2.00 µC and -2.00 µC,respectively.What is the electric field at a point midway between the two charges? (k_e = 8.99 x 10⁹ N·m²/C²)