Question 1

A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = -3 m to y = 2m.Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?

Accepted Answer

A)  $\int _ { - 3 } ^ { 2 } \frac { 27 d y } { ( 4 - y ) ^ { 2 } }$ 
B)  $\int _ { - 3 } ^ { 2 } \frac { 27 d y } { 16 + y ^ { 2 } }$ 
C)  $$\int _ { - 3 } ^ { 2 } \frac { 135 d y } { ( 4 - y ) ^ { 2 } }$$ 
D)  $\int _ { - 3 } ^ { 2 } \frac { 135 d y } { 16 + y ^ { 2 } }$ 
E) none of these

Question 2

A particle (mass = 5.0 g,charge = 40 mC)moves in a region of space where the electric field is uniform and is given by Ex = 2.5 N/C,Ey = Ez = 0.If the velocity of the particle at t = 0 is given by vy = 50 m/s,vx = vz = 0,what is the speed of the particle at t = 2.0 s?

Accepted Answer

A) 81 m/s 
B) 72 m/s 
C) 64 m/s 
D) 89 m/s 
E) 25 m/s

Question 3

The axis of a long hollow metallic cylinder (inner radius = 1.0 cm,outer radius = 2.0 cm)coincides with a long wire.The wire has a linear charge density of -8.0 pC/m,and the cylinder has a net charge per unit length of -4.0 pC/m.Determine the magnitude of the electric field 3.0 cm from the axis.

Accepted Answer

A) 5.4 N/C 
B) 7.2 N/C 
C) 4.3 N/C 
D) 3.6 N/C 
E) 2.4 N/C

Question 4

A solid nonconducting sphere (radius = 12 cm)has a charge of uniform density (30 nC/m3)distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

Accepted Answer

A) 22 N/C 
B) 49 N/C 
C) 31 N/C 
D) 87 N/C 
E) 26 N/C

Question 5

Three point charges,two positive and one negative,each having a magnitude of 20 $\mu$C 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

A) 80 N 
B) 40 N 
C) 69 N 
D) 57 N 
E) 75 N

Question 6

A point charge (5.0 pC)is located at the center of a spherical surface (radius = 2.0 cm),and a charge of 3.0 pC is spread uniformly upon this surface.Determine the magnitude of the electric field 1.0 cm from the point charge.

Accepted Answer

A) 0.72 kN/C 
B) 0.45 kN/C 
C) 0.63 kN/C 
D) 0.90 kN/C 
E) 0.18 kN/C

Question 7

Charge of uniform density 4.0 nC/m is distributed along the x axis from x = -2.0 m to x = +3.0 m.What is the magnitude of the electric field at the point x = +5.0 m on the x axis?

Accepted Answer

A) 16 N/C 
B) 13 N/C 
C) 19 N/C 
D) 26 N/C 
E) 5.0 N/C

Question 8

A charge (uniform linear density = 9.0 nC/m)is distributed along the x axis from x = 0 to x = 3.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.

Accepted Answer

A) 81 N/C 
B) 74 N/C 
C) 61 N/C 
D) 88 N/C 
E) 20 N/C

Question 9

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

A) Y has a negative charge. 
B) Z has a negative charge. 
C) Y has a positive charge. 
D) Z has a positive charge. 
E) Z is neutral (has no net charge. )

Question 10

A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m.What is the magnitude of the electric field at the origin?

Accepted Answer

A) 18 N/C 
B) 50 N/C 
C) 30 N/C 
D) 15 N/C 
E) 90 N/C

Question 11

A particle (m = 20 mg,q = -5.0 $\mu$C)moves in a uniform electric field of 60 N/C in the positive x direction.At t = 0,the particle is moving 25 m/s in the positive x direction and is passing through the origin.How far is the particle from the origin at t = 2.0 s?

Accepted Answer

A) 80 m 
B) 20 m 
C) 58 m 
D) 10 m 
E) 30 m

Question 12

A point charge Q is placed at the origin.A second charge,2Q,is placed on the x axis at x = -3.0 m.If Q = 50 $\mu$C,what is the magnitude of the electrostatic force on a third point charge,-Q,placed on the y axis at y = +4.0 m?

Accepted Answer

A) 2.5 N 
B) 3.0 N 
C) 3.7 N 
D) 4.4 N 
E) 1.8 N

Question 13

A +15-nC point charge is placed on the x axis at x = 1.5 m,and a -20-nC charge is placed on the y axis at y = -2.0m.What is the magnitude of the electric field at the origin?

Accepted Answer

A) 105 N/C 
B) 15 N/C 
C) 75 N/C 
D) 45 N/C 
E) 60 N/C

Question 14

A particle (mass = 5.0 g,charge = 40 mC)moves in a region of space where the electric field is uniform and is given by Ex =-2.3 N/C,Ey = Ez = 0.If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and vz = 20 m/s,vx = vy = 0,what is the distance from the origin to the particle at t = 2.0 s?

Accepted Answer

A) 60 m 
B) 54 m 
C) 69 m 
D) 78 m 
E) 3.2 m

Question 15

A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m.Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?

Accepted Answer

A)  $\int _ { 0 } ^ { 4 } \frac { 216 d y } { \left( 4 + y ^ { 2 } \right) ^ { 3 / 2 } }$ 
B)  $\int _ { 0 } ^ { 4 } \frac { 54 d y } { \left( 4 + y ^ { 2 } \right) ^ { 3 / 2 } }$ 
C)  $\int _ { 0 } ^ { 4 } \frac { 108 d y } { 4 + y ^ { 2 } }$ 
D)  $\int _ { 0 } ^ { 4 } \frac { 27 d y } { 4 + y ^ { 2 } }$ 
E) none of these

Question 16

Gino says that the analog of Gauss's law for the flow of an incompressible fluid of density$\nu$ at constant velocity $\overrightarrow { \mathbf { v } }$ is $\oint \rho\overrightarrow { \mathbf { v } } \cdot d \mathbf { A } = 0$ for an imaginary surface within the fluid.Lorenzo says that it is true only if the area where the fluid enters the surface and the area where it leaves the surface are both perpendicular to the velocity of the fluid.Which one,if either,is correct?

Accepted Answer

A) Gino,because as much fluid leaves as enters. 
B) Lorenzo,because $\oint \rho\overrightarrow { \mathbf { v } } \cdot d \mathbf { A }$ is not equal to zero if the fluid enters or exits at angles other than 90$\degree$. 
C) Lorenzo,because this is true only when the fluid executes rotational motion. 
D) Gino,because it is true only when the fluid is enclosed on all sides,not when it is flowing. 
E) Lorenzo,because it is true only when the fluid is enclosed on all sides,not when it is flowing.

Exam 19: Electric Forces and Electric Fields

A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = -3 m to y = 2m.Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?

A particle (mass = 5.0 g,charge = 40 mC) moves in a region of space where the electric field is uniform and is given by E_x = 2.5 N/C,E_y = E_z = 0.If the velocity of the particle at t = 0 is given by v_y = 50 m/s,v_x = v_z = 0,what is the speed of the particle at t = 2.0 s?

The axis of a long hollow metallic cylinder (inner radius = 1.0 cm,outer radius = 2.0 cm) coincides with a long wire.The wire has a linear charge density of -8.0 pC/m,and the cylinder has a net charge per unit length of -4.0 pC/m.Determine the magnitude of the electric field 3.0 cm from the axis.

A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m³) distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

Three point charges,two positive and one negative,each having a magnitude of 20 $\mu$ C 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 (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm) ,and a charge of 3.0 pC is spread uniformly upon this surface.Determine the magnitude of the electric field 1.0 cm from the point charge.

Charge of uniform density 4.0 nC/m is distributed along the x axis from x = -2.0 m to x = +3.0 m.What is the magnitude of the electric field at the point x = +5.0 m on the x axis?

A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.

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

A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m.What is the magnitude of the electric field at the origin?

A particle (m = 20 mg,q = -5.0 $\mu$ C) moves in a uniform electric field of 60 N/C in the positive x direction.At t = 0,the particle is moving 25 m/s in the positive x direction and is passing through the origin.How far is the particle from the origin at t = 2.0 s?

A point charge Q is placed at the origin.A second charge,2Q,is placed on the x axis at x = -3.0 m.If Q = 50 $\mu$ C,what is the magnitude of the electrostatic force on a third point charge,-Q,placed on the y axis at y = +4.0 m?

A +15-nC point charge is placed on the x axis at x = 1.5 m,and a -20-nC charge is placed on the y axis at y = -2.0m.What is the magnitude of the electric field at the origin?

A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m.Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?

Exam 19: Electric Forces and Electric Fields

A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = -3 m to y = 2m.Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?

A particle (mass = 5.0 g,charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.5 N/C,Ey = Ez = 0.If the velocity of the particle at t = 0 is given by vy = 50 m/s,vx = vz = 0,what is the speed of the particle at t = 2.0 s?

The axis of a long hollow metallic cylinder (inner radius = 1.0 cm,outer radius = 2.0 cm) coincides with a long wire.The wire has a linear charge density of -8.0 pC/m,and the cylinder has a net charge per unit length of -4.0 pC/m.Determine the magnitude of the electric field 3.0 cm from the axis.

A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m3) distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

Three point charges,two positive and one negative,each having a magnitude of 20 μ\muμ C 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 (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm) ,and a charge of 3.0 pC is spread uniformly upon this surface.Determine the magnitude of the electric field 1.0 cm from the point charge.

Charge of uniform density 4.0 nC/m is distributed along the x axis from x = -2.0 m to x = +3.0 m.What is the magnitude of the electric field at the point x = +5.0 m on the x axis?

A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.

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

A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m.What is the magnitude of the electric field at the origin?

A particle (m = 20 mg,q = -5.0 μ\muμ C) moves in a uniform electric field of 60 N/C in the positive x direction.At t = 0,the particle is moving 25 m/s in the positive x direction and is passing through the origin.How far is the particle from the origin at t = 2.0 s?

A point charge Q is placed at the origin.A second charge,2Q,is placed on the x axis at x = -3.0 m.If Q = 50 μ\muμ C,what is the magnitude of the electrostatic force on a third point charge,-Q,placed on the y axis at y = +4.0 m?

A +15-nC point charge is placed on the x axis at x = 1.5 m,and a -20-nC charge is placed on the y axis at y = -2.0m.What is the magnitude of the electric field at the origin?

A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m.Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?

A particle (mass = 5.0 g,charge = 40 mC) moves in a region of space where the electric field is uniform and is given by E_x = 2.5 N/C,E_y = E_z = 0.If the velocity of the particle at t = 0 is given by v_y = 50 m/s,v_x = v_z = 0,what is the speed of the particle at t = 2.0 s?

A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m³) distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

Three point charges,two positive and one negative,each having a magnitude of 20 $\mu$ C 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 particle (m = 20 mg,q = -5.0 $\mu$ C) moves in a uniform electric field of 60 N/C in the positive x direction.At t = 0,the particle is moving 25 m/s in the positive x direction and is passing through the origin.How far is the particle from the origin at t = 2.0 s?

A point charge Q is placed at the origin.A second charge,2Q,is placed on the x axis at x = -3.0 m.If Q = 50 $\mu$ C,what is the magnitude of the electrostatic force on a third point charge,-Q,placed on the y axis at y = +4.0 m?