Question 1

Four electric fields,E₁,E₂,E_3, and E₄ are produced at four different points,1,2,3,and 4 by charges q,2q,q,and 2q,respectively.If the distances of the four points from the charges are 10,10,20,and 20 cm,respectively,rank in order from smallest to largest their electric field strengths.

Accepted Answer

The electric field strength (E) due to a point charge (q) at a distance (r) is given by E = kq/r^2, where k is Coulomb's constant. For points 1 and 2, the charges are q and 2q at the same distance (10 cm), so E2 > E1 due to the larger charge. For points 3 and 4, the charges are q and 2q at the same distance (20 cm), so E4 > E3 due to the larger charge. Since the distances for points 3 and 4 are double that of points 1 and 2, their electric fields will be weaker due to the r^2 term in the denominator, making E3 the weakest and E2 the strongest.

Question 2

A solid,insulating sphere of radius a = 2 cm has a total charge Q = 10 nC which is uniformly distributed.Using Gauss's Law determine the magnitude of the electric field at a point inside sphere which is 1 cm from its center.

Accepted Answer

Using Gauss's Law, the electric field inside a uniformly charged sphere is given by E = (1/4πε₀) * (Qr/a³), where r is the distance from the center. Substituting the given values, E = (1/4πε₀) * (10 * 10⁻⁹ C * 0.01 m / (0.02 m)³) = 1.13 * 10⁵ N/C.

Question 3

A thin glass rod is bent into a semicircle of radius R.A charge + Q is uniformly distributed along the upper half,and a charge -Q is uniformly distributed along the lower half,as shown in the figure.If R = 10 cm and the electric field E at point P is 4.81 * 10⁴ N/C in -y direction,what is the charge,Q? Point P is at the center of the semicircle.

Accepted Answer

The electric field at point P due to a semicircle of radius R and charge +Q is given by
E1 =

where k is the Coulomb constant, R is the radius of the semicircle, and Q is the charge on the semicircle.

Similarly, the electric field at point P due to a semicircle of radius R and charge -Q is given by
E2 =

Since the two semicircles are symmetric with respect to the x-axis, the net electric field at point P is in the -y direction and is given by the difference of the two electric fields:

E = E1 - E2 =

Substituting the given values of R and E and solving for Q, we get:

Q =

Q ≈ 42 nC

Therefore, the best choice is C.

Question 4

Three + 4.0-mC fixed point charges are located at (0.0 mm,0.0 mm),(2.0 mm,2.0 mm),and (2.0 mm,-2.0 mm).What is the magnitude of the electric field at the position (2.0 mm,0.0 mm)?

Accepted Answer

The answer of Three + 4.0-mC fixed point charges are...

Question 5

The electrons in a particle beam enter an electric field of 2000 N/C and are stopped in a distance of 1 m.What was the kinetic energy of one of these electrons prior to entering the electric field?

Accepted Answer

The answer of The electrons in a particle beam enter...

Question 6

A thin glass rod is bent into a semicircle of radius R.A charge + Q is uniformly distributed along the upper half,and a charge -Q is uniformly distributed along the lower half,as shown in the figure.If Q = 10 nC and the electric field E at point P is 5.85 * 10⁴ N/C in -y direction,what is the radius of the semicircle,R? Point P is at the center of the semicircle.

Accepted Answer

The answer of A thin glass rod is bent into...

Question 7

Consider the Earth to have a uniformly charged surface with density  $\sigma$ per unit area.What is the value of  $\sigma$ if objects near the surface,carrying charge Q and having mass m,experience no net force?

Accepted Answer

The answer of Consider the Earth to have a uniformly...

Question 8

A thin glass rod is bent into a semicircle of radius R.A charge + Q is uniformly distributed along the upper half,and a charge -Q is uniformly distributed along the lower half,as shown in the figure.If Q = 10 nC and R = 10 cm,find the magnitude and direction of the electric field E (in component form)at point P,the center of the semicircle.

Accepted Answer

The answer of A thin glass rod is bent into...

Question 9

An electric dipole is placed into a uniform electric field directed to the right as shown in the figure.What motion will the dipole have in this electric field?

Accepted Answer

An electric dipole in a uniform electric field experiences a torque that attempts to align the dipole moment vector with the direction of the electric field. In this case, the dipole moment vector would try to align with the direction of the uniform field, leading to a rotation in a counter-clockwise direction. There would be no net translational motion of the dipole. Therefore, the correct answer is D.

Question 10

The electrons in a particle beam each have a kinetic energy of 1.6 * 10^-16 J.The magnitude of the electric field that would stop the electrons in a distance of 1 m is

Accepted Answer

The kinetic energy of an electron equals to the work done by the electric field in bringing it from rest to the given speed. Therefore, we can use the work-energy theorem to find the electric field:

K = q * V = W = F * d

where K is the kinetic energy of the electron, q is the electron charge, V is the potential difference across the plates of length d that stop the electron, and F is the electric force on the electron.

Rearranging the equation, we get:

F = K / d * q

Substituting the given values, we get:

F = (1.6 x 10^-16 J) / (1 m) * (1.6 x 10^-19 C) = 1000 N/C

Therefore, the magnitude of the electric field that would stop the electrons in a distance of 1 m is 1000 N/C, which corresponds to choice B.

Question 11

A point charge q is located at the center of a sphere of radius R.Also concentrically inside the sphere is a uniform ring having linear charge density $\lambda$ and radius a (a <R).The flux through the sphere is

Accepted Answer

The answer of A point charge q is located at...

Question 12

A point charge q is located at the center of a sphere of radius R.The sphere is then surrounded concentrically by a uniform ring having linear charge density $\lambda$ and radius a (a >R).The flux through the sphere is

Accepted Answer

Gauss's law states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. Since only the point charge q is enclosed by the sphere, the flux through the sphere depends solely on q, regardless of any external charges.

Question 13

A spherical Gaussian surface of radius R surrounds a point charge Q.If the radius of the sphere is doubled,the electric flux through its surface is

Accepted Answer

Electric flux through a spherical Gaussian surface only depends on the charge enclosed by the surface. Since we are not changing the charge Q, the flux remains the same even if the radius of the sphere is doubled. Therefore, the correct choice is E (the same).

Question 14

The electric field is zero at some point on a line that runs between the centers of two charged spheres.What can one say about this situation?

Accepted Answer

The electric field is zero at a point between two charges when the charges have the same sign, as the fields due to each charge can cancel each other out at some point along the line between them.

Question 15

A cannon shoots 5.0-kg cannon ball that carries a charge of 3.0 Coulombs at some angle above horizontal ground in a region in which there is a uniform electric field E and gravitational acceleration is straight down,-9.8 m/s² ŷ.If the ball travels half the horizontal distance before striking the ground that it would have if there were no electric field,what is the magnitude of the electric field?

Accepted Answer

The answer of A cannon shoots 5.0-kg cannon ball that...

Question 16

The electrons in a particle beam each have a kinetic energy of 1.6 * 10^-16 J,enter an electric field of 2000 N/C and are stopped.What is the stopping distance of these electrons?

Accepted Answer

The answer of The electrons in a particle beam each...

Question 17

A cannon shoots a charged,5.0-kg cannon ball at some angle above horizontal ground in a region in which the electric field is given by 12.0 N/C ŷ,while gravitational acceleration is straight down,-9.8 m/s² ŷ.If the ball travels half the distance it would have if there were no electric field,what is the charge on the cannon ball?

Accepted Answer

The electric field exerts an upward force on the charged cannonball, counteracting gravity. To reduce the range by half, the electric force must equal the gravitational force. Solving for charge using F = qE = mg gives q = -mg/E = -(5.0 kg)(9.8 m/s²)/(12.0 N/C) = -4.1 C.

Question 18

A small metal ball with a mass of 10 grams and a charge of 5.0 mC is located in a region of space with an electric field of 12 N/C directed to the east.The ball is released from rest at a distance of 30 cm above the ground.What is the speed of the ball just before it hits the ground?

Accepted Answer

First, let's calculate the electric force acting on the ball:
F = qE
F = (5.0 × 10^-3 C)(12 N/C) = 0.06 N

Next, let's find the acceleration of the ball using Newton's second law:
F = ma
a = F/m
a = (0.06 N)/(0.01 kg) = 6 m/s^2

Now, let's find the distance the ball falls before hitting the ground:
d = 0.3 m

Finally, we can use the kinematic equation to find the final velocity:
v^2 = vi^2 + 2ad
vi = 0 m/s (since the ball is released from rest)
v^2 = 2(6 m/s^2)(0.3 m) = 3.6 m^2/s^2
v = √(3.6 m^2/s^2) = 1.9 m/s

Therefore, the best choice is D, 2.8 m/s (rounded to one significant figure).

Question 19

Four electric fields,E₁,E₂,E_3, and E₄ are produced at four different points,1,2,3,and 4 by charges q,2q,q,and 2q,respectively.If the distances of the four points from the charges are 10,10,20,and 20 cm,respectively,rank in order from largest to smallest their electric field strengths.

Accepted Answer

The electric field strength (E) due to a point charge (q) is given by E = kq/r^2, where k is Coulomb's constant and r is the distance from the charge. For points 1 and 3 (with charges q and q, respectively), the electric field strength at point 1 will be greater than at point 3 because they have the same charge but point 1 is closer. For points 2 and 4 (with charges 2q and 2q, respectively), the electric field strength at point 2 will be greater than at point 4 for the same reason. Comparing points 1 and 2 (or 3 and 4), the electric field strength at point 2 (or 4) will be greater because the charge is double that at point 1 (or 3), and they are at the same distance. Therefore, the ranking from largest to smallest electric field strengths is ES2 > ES1 > ES4 > ES3.

Question 20

An insulating solid sphere of radius a has a uniform volume charge density $\rho$ and total positive charge q.The strength of the electric field inside the sphere at a distance r from the center (r < a)is proportional to

Accepted Answer

For a uniformly charged solid sphere, the electric field inside the sphere is given by:
E = (1/3ε₀) * (q/a³) * r
Since the electric field is directly proportional to r, the correct choice is B.

Quiz 22: Electric Fields and Gausss Law

Four electric fields,E₁,E₂,E_3, and E₄ are produced at four different points,1,2,3,and 4 by charges q,2q,q,and 2q,respectively.If the distances of the four points from the charges are 10,10,20,and 20 cm,respectively,rank in order from smallest to largest their electric field strengths.

A solid,insulating sphere of radius a = 2 cm has a total charge Q = 10 nC which is uniformly distributed.Using Gauss's Law determine the magnitude of the electric field at a point inside sphere which is 1 cm from its center.

Three + 4.0-mC fixed point charges are located at (0.0 mm,0.0 mm) ,(2.0 mm,2.0 mm) ,and (2.0 mm,-2.0 mm) .What is the magnitude of the electric field at the position (2.0 mm,0.0 mm) ?

The electrons in a particle beam enter an electric field of 2000 N/C and are stopped in a distance of 1 m.What was the kinetic energy of one of these electrons prior to entering the electric field?

Consider the Earth to have a uniformly charged surface with density $\sigma$ per unit area.What is the value of $\sigma$ if objects near the surface,carrying charge Q and having mass m,experience no net force?

An electric dipole is placed into a uniform electric field directed to the right as shown in the figure.What motion will the dipole have in this electric field?

The electrons in a particle beam each have a kinetic energy of 1.6 * 10^-16 J.The magnitude of the electric field that would stop the electrons in a distance of 1 m is

A point charge q is located at the center of a sphere of radius R.Also concentrically inside the sphere is a uniform ring having linear charge density $\lambda$ and radius a (a <R) .The flux through the sphere is

A point charge q is located at the center of a sphere of radius R.The sphere is then surrounded concentrically by a uniform ring having linear charge density $\lambda$ and radius a (a >R) .The flux through the sphere is

A spherical Gaussian surface of radius R surrounds a point charge Q.If the radius of the sphere is doubled,the electric flux through its surface is

The electric field is zero at some point on a line that runs between the centers of two charged spheres.What can one say about this situation?

The electrons in a particle beam each have a kinetic energy of 1.6 * 10^-16 J,enter an electric field of 2000 N/C and are stopped.What is the stopping distance of these electrons?

A small metal ball with a mass of 10 grams and a charge of 5.0 mC is located in a region of space with an electric field of 12 N/C directed to the east.The ball is released from rest at a distance of 30 cm above the ground.What is the speed of the ball just before it hits the ground?

Four electric fields,E₁,E₂,E_3, and E₄ are produced at four different points,1,2,3,and 4 by charges q,2q,q,and 2q,respectively.If the distances of the four points from the charges are 10,10,20,and 20 cm,respectively,rank in order from largest to smallest their electric field strengths.

An insulating solid sphere of radius a has a uniform volume charge density $\rho$ and total positive charge q.The strength of the electric field inside the sphere at a distance r from the center (r < a) is proportional to

Quiz 22: Electric Fields and Gausss Law

Four electric fields,E1,E2,E3, and E4 are produced at four different points,1,2,3,and 4 by charges q,2q,q,and 2q,respectively.If the distances of the four points from the charges are 10,10,20,and 20 cm,respectively,rank in order from smallest to largest their electric field strengths.

A solid,insulating sphere of radius a = 2 cm has a total charge Q = 10 nC which is uniformly distributed.Using Gauss's Law determine the magnitude of the electric field at a point inside sphere which is 1 cm from its center.

Three + 4.0-mC fixed point charges are located at (0.0 mm,0.0 mm) ,(2.0 mm,2.0 mm) ,and (2.0 mm,-2.0 mm) .What is the magnitude of the electric field at the position (2.0 mm,0.0 mm) ?

The electrons in a particle beam enter an electric field of 2000 N/C and are stopped in a distance of 1 m.What was the kinetic energy of one of these electrons prior to entering the electric field?

Consider the Earth to have a uniformly charged surface with density σ\sigmaσ per unit area.What is the value of σ\sigmaσ if objects near the surface,carrying charge Q and having mass m,experience no net force?

An electric dipole is placed into a uniform electric field directed to the right as shown in the figure.What motion will the dipole have in this electric field?

The electrons in a particle beam each have a kinetic energy of 1.6 * 10-16 J.The magnitude of the electric field that would stop the electrons in a distance of 1 m is

A point charge q is located at the center of a sphere of radius R.Also concentrically inside the sphere is a uniform ring having linear charge density λ\lambdaλ and radius a (a <R) .The flux through the sphere is

A point charge q is located at the center of a sphere of radius R.The sphere is then surrounded concentrically by a uniform ring having linear charge density λ\lambdaλ and radius a (a >R) .The flux through the sphere is

A spherical Gaussian surface of radius R surrounds a point charge Q.If the radius of the sphere is doubled,the electric flux through its surface is

The electric field is zero at some point on a line that runs between the centers of two charged spheres.What can one say about this situation?

The electrons in a particle beam each have a kinetic energy of 1.6 * 10-16 J,enter an electric field of 2000 N/C and are stopped.What is the stopping distance of these electrons?

A small metal ball with a mass of 10 grams and a charge of 5.0 mC is located in a region of space with an electric field of 12 N/C directed to the east.The ball is released from rest at a distance of 30 cm above the ground.What is the speed of the ball just before it hits the ground?

Four electric fields,E1,E2,E3, and E4 are produced at four different points,1,2,3,and 4 by charges q,2q,q,and 2q,respectively.If the distances of the four points from the charges are 10,10,20,and 20 cm,respectively,rank in order from largest to smallest their electric field strengths.

An insulating solid sphere of radius a has a uniform volume charge density ρ\rhoρ and total positive charge q.The strength of the electric field inside the sphere at a distance r from the center (r < a) is proportional to

Four electric fields,E₁,E₂,E_3, and E₄ are produced at four different points,1,2,3,and 4 by charges q,2q,q,and 2q,respectively.If the distances of the four points from the charges are 10,10,20,and 20 cm,respectively,rank in order from smallest to largest their electric field strengths.

Consider the Earth to have a uniformly charged surface with density $\sigma$ per unit area.What is the value of $\sigma$ if objects near the surface,carrying charge Q and having mass m,experience no net force?

The electrons in a particle beam each have a kinetic energy of 1.6 * 10^-16 J.The magnitude of the electric field that would stop the electrons in a distance of 1 m is

A point charge q is located at the center of a sphere of radius R.Also concentrically inside the sphere is a uniform ring having linear charge density $\lambda$ and radius a (a <R) .The flux through the sphere is

A point charge q is located at the center of a sphere of radius R.The sphere is then surrounded concentrically by a uniform ring having linear charge density $\lambda$ and radius a (a >R) .The flux through the sphere is

The electrons in a particle beam each have a kinetic energy of 1.6 * 10^-16 J,enter an electric field of 2000 N/C and are stopped.What is the stopping distance of these electrons?

Four electric fields,E₁,E₂,E_3, and E₄ are produced at four different points,1,2,3,and 4 by charges q,2q,q,and 2q,respectively.If the distances of the four points from the charges are 10,10,20,and 20 cm,respectively,rank in order from largest to smallest their electric field strengths.

An insulating solid sphere of radius a has a uniform volume charge density $\rho$ and total positive charge q.The strength of the electric field inside the sphere at a distance r from the center (r < a) is proportional to