4.16×10^42 (1.1)

It is known that the electric force of repulsion between two electrons is much stronger than the gravitational attraction. For two electrons at a distance d apart, calculate the ratio of the size of the electrostatic repulsion to that of the gravitational attraction.

Use the following data:

k = 8.99×109 Nm2/C2, e = 1.60×10-19 C,

G = 6.67×10-11 Nm2/kg2, me = 9.11×10-31 kg.

Use the following data:

k = 8.99×109 Nm2/C2, e = 1.60×10-19 C,

G = 6.67×10-11 Nm2/kg2, me = 9.11×10-31 kg.

18.40 C (1.2)

The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. Assume that these protons are incident on the Earth’s atmosphere from all directions at a rate of 1336. protons per square meter per second. Assuming that the depth of Earth’s atmosphere is 120.0 km, what is the total charge incident on the atmosphere in 162.0 s? Assume that the radius of the surface of the Earth is 6378. km.

A)2.70×10^-8 C

B) No

(1.3)

B) No

(1.3)

A) In the figure, two conducting balls of identical mass m = 25g and identical charge q hang from nonconducting threads of length L = 120cm.

If x = 4.0cm, what is q? Since x is much smaller than L approximate sin(θ) by θ.

B) Do we know the sign of q? (positive, negative, no)

If x = 4.0cm, what is q? Since x is much smaller than L approximate sin(θ) by θ.

B) Do we know the sign of q? (positive, negative, no)

1.49 N (1.4)

Four equal charges of +1.1×10-6 C are placed on the corners of one face of a cube of edge length 15.0 cm. A charge of -1.1×10-6 C is placed at the center of the cube. What is the magnitude of the force on the charge at the center of the cube?

A) 3.80×10^-6 C

B) 4.80×10^-6 C

(1.5)

B) 4.80×10^-6 C

(1.5)

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.6559 N when separated by 50 cm, center-to-center. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0090 N. What were the initial charges on the spheres? Since one is negative and you cannot tell which is positive or negative, there are two solutions.

A) What is the smaller value?

B What is the larger value?

A) What is the smaller value?

B What is the larger value?

A) 4.790×10^-8 C

B) 2.724×10^-19 kg

(1.6)

B) 2.724×10^-19 kg

(1.6)

A 15.9-g mass is suspended 1.15 cm above a nonconducting flat plate, directly above an embedded charge of q.

A) If the mass has the same charge, q, how much must q be so that the mass levitates (just floats, neither rising nor falling)?

B) If the charge q is produced by adding electrons to the mass, by how much will the mass be changed?

1.15×10^-6 N (1.7)

Three equal charges are placed at the corners of an equilateral triangle 0.50 m on a side. What are the magnitude of the force on each charge if the charges are each -4.3×10-9 C?

A) 0 m

B) 3.373 m

(1.8)

B) 3.373 m

(1.8)

A positive charge Q = 21.5 μC is on the y-axis at a distance a = 4.77 m from the origin, and another positive charge q = 0.53 μC is on the x-axis at a distance b from the origin.

A) For what value(s) of b is the x-component of the force on q a minimum?

B) For what value(s) of b is the x-component of the force on q a maximum?

7.559 nC

(1.9)

(1.9)

In the figure, the net electrostatic force on charge QA is zero. If QA = +5.27 nC and Q = -2.49 nC, determine Q0.

-28.0 cm

(1.10)

(1.10)

A positive charge q1 = 1.47 μC is fixed at the origin, and a second charge q2 = -2.75 μC is fixed at x = 10.3 cm. Where along the x-axis should a third charge be positioned so that it experiences no force?

A) 2.99×10^-14 N

B) 4.14×10^2

(2.2)

B) 4.14×10^2

(2.2)

A spherical water drop, 1.80 μm in diameter, is suspended in calm air owing to a downward-directed atmospheric electric field E = 452 N/C.

A) What is the weight of the drop?

B) How many excess electrons does the drop have?

A) What is the weight of the drop?

B) How many excess electrons does the drop have?

A) Yes, it strikes. Horizontal distance = 2.92×10^-2 m

B) No, it doesn’t strike. Vertical Position = 1.16×10^-2 m

(2.3)

B) No, it doesn’t strike. Vertical Position = 1.16×10^-2 m

(2.3)

In the figure, a uniform, upward-pointing electric field E of magnitude 1.50×103 N/C has been set up between two horizontal plates by charging the lower plate positively and the upper plate negatively. The plates have length L = 4 cm and separation d = 2.00 cm. Electrons are shot between the plates from the left edge of the lower plate.

The first electron has the initial velocity v0, which makes an angle θ=45° with the lower plate and has a magnitude of 4.94×106 m/s.

A) Will this electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates.

B) Another electron has an initial velocity which has the angle θ=45° with the lower plate and has a magnitude of 3.85×106 m/s. Will this electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates.

The first electron has the initial velocity v0, which makes an angle θ=45° with the lower plate and has a magnitude of 4.94×106 m/s.

A) Will this electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates.

B) Another electron has an initial velocity which has the angle θ=45° with the lower plate and has a magnitude of 3.85×106 m/s. Will this electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates.

1.90×10^-1 m

(2.4)

(2.4)

A positive charge of 0.900μ C is located in a uniform field of 1.00×105 N/C. A negative charge of -0.400μ C is brought near enough to the positive charge that the attractive force between the charges just equals the force on the positive charge due to the field. How close are the two charges?

A) 4.29×10^8 N/C

B) 2.32×10^8 N/C

C) 4.88×10^8 N/C

(2.5)

B) 2.32×10^8 N/C

C) 4.88×10^8 N/C

(2.5)

In the figure, four charges, given in multiples of 1.00×10-5 C form the corners of a square and four more charges lie at the midpoints of the sides of the square. The distance between adjacent charges on the perimeter of the square is d = 3.70×10-2 m.

A) What is Ex?

B) What it Ey?

C) What is the magnitude of E?

A) What is Ex?

B) What it Ey?

C) What is the magnitude of E?

46.5079 N/C

(2.6)

(2.6)

As shown in the figure above, a ball of mass 0.6 g and positive charge q =33.9 μC is suspended on a string of negligible mass in a uniform electric field. We observe that the ball hangs at an angle of ϑ=15.0 degrees from the vertical. What is the magnitude of the electric field?

A) 0.00 N/C

B) -5.30×10^6 N/C (2.7)

B) -5.30×10^6 N/C (2.7)

In the figure (a), two curved plastic rods, one of charge +q = 1.50×10-5 C and the other of charge -q, form a circle of radius R = 0.18 m in an xy plane. The x axis passes through their connecting points, and the charge is distributed uniformly on both rods. What are the magnitude and direction of the electric field E produced at P, the center of the circle?

A) Ex?

B) Ey?

A) Ex?

B) Ey?

1.175×10^5 N/C (2.8)

A charge per unit length λ = +6.00 μC/m is uniformly distributed along the positive y-axis from y = 0 to y = +a = +0.500 m. A charge per unit length λ = -6.00 μC/m, is uniformly distributed along the negative y-axis from y = 0 to y = -a = -0.500 m. What is the magnitude of the electric field at a point on the x-axis a distance x = 0.371 m from the origin?

A) 0 Nm^2/C

B) -5.88 Nm^2/C

C) 0 Nm^2/C

D) 0 Nm^2/C (No Flux when E is constant or in closed surface)

(3.2)

B) -5.88 Nm^2/C

C) 0 Nm^2/C

D) 0 Nm^2/C (No Flux when E is constant or in closed surface)

(3.2)

A cube with 1.40 m edges is oriented as shown in the figure in a region of uniform electric field.

A) Find the electric flux through the right face if the electric field, in newtons per coulomb ( N/C), is given by 3.20i. (N*m(shift-6)2/C)

B) Find the electric flux through the right face if the electric field, in newtons per coulomb ( N/C), is given by -3.00j.

C) Find the electric flux through the right face if the electric field, in newtons per coulomb ( N/C), is given by -2.40i + 5.20k.

D) What is the total flux through the cube for each of these fields?

A) Find the electric flux through the right face if the electric field, in newtons per coulomb ( N/C), is given by 3.20i. (N*m(shift-6)2/C)

B) Find the electric flux through the right face if the electric field, in newtons per coulomb ( N/C), is given by -3.00j.

C) Find the electric flux through the right face if the electric field, in newtons per coulomb ( N/C), is given by -2.40i + 5.20k.

D) What is the total flux through the cube for each of these fields?

A) 0 Nm^2/C (B/c The charge touches side A)

B) 94.1×10^4 Nm^2/C (B/c broken into 8 parts and multiplied by three faces not touching charge)

(3.3)

B) 94.1×10^4 Nm^2/C (B/c broken into 8 parts and multiplied by three faces not touching charge)

(3.3)

A point charge q = 8.70×10-6 C is placed at one corner of a cube of edge a = 0.26 m. What is the flux through each of the cube faces? See the figure. (Hint: Use Gauss’ law and symmetry arguments.)

A) What is the flux through side A?

B) What is the flux through side B?

A) What is the flux through side A?

B) What is the flux through side B?

A) 3.84×10^7 N/C

B) 2.15×10^1 N/C

(3.4)

B) 2.15×10^1 N/C

(3.4)

A square metal plate of edge length 9.0 cm and negligible thickness has a total charge of 5.50×10-6 C.

A) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.50 mm) by assuming that the charge is spread uniformly over the two faces of the plate.

B) Estimate E at a distance of 48 m (large relative to the plate size) by assuming that the plate is a point charge.

A) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.50 mm) by assuming that the charge is spread uniformly over the two faces of the plate.

B) Estimate E at a distance of 48 m (large relative to the plate size) by assuming that the plate is a point charge.

A) 1.3×10^8 N/C

B) 2.6×10^8 N/C

(3.5)

B) 2.6×10^8 N/C

(3.5)

A planar slab of thickness of 5.00 cm has a uniform volume charge density of 9.20×10-2 C/ m3.

A) Find the magnitude of the electric field at all points in space both inside and outside the slab, in terms of x, the distance measured from the central plane of the slab. What is the field for x = 1.25 cm?

B) What is the field for x = 10.00 cm?

A) Find the magnitude of the electric field at all points in space both inside and outside the slab, in terms of x, the distance measured from the central plane of the slab. What is the field for x = 1.25 cm?

B) What is the field for x = 10.00 cm?

A) 0 N/C

B) 2.33×10^7 N/C

C) 6.94×10^6 N/C

D) 4.0×10^-6 N/C

(3.6)

B) 2.33×10^7 N/C

C) 6.94×10^6 N/C

D) 4.0×10^-6 N/C

(3.6)

A thin, metallic, spherical shell of radius a = 2.0 cm has a charge qa = 3.00×10-6 C. Concentric with it is another thin, metallic, spherical shell of radius b = 4.80 cm and charge qb = 1.00×10-6 C.

A) Find the electric field at radial points r where r = 0.0 cm

B) Find the electric field at radial points r where r = 3.4 cm.

C) Find the electric field at radial points r where r = 7.2 cm.

D) Discuss the criterion one would use to determine how the charges are distributed on the inner and outer surface of the shells. What is the charge on the outer surface of the outer shell?

A) Find the electric field at radial points r where r = 0.0 cm

B) Find the electric field at radial points r where r = 3.4 cm.

C) Find the electric field at radial points r where r = 7.2 cm.

D) Discuss the criterion one would use to determine how the charges are distributed on the inner and outer surface of the shells. What is the charge on the outer surface of the outer shell?

A) -2.5×10^-6 C

B) 1.25×10^-5 C

(3.7)

B) 1.25×10^-5 C

(3.7)

An isolated conductor of arbitrary shape has a net charge of +1.00×10-5 C. Inside the conductor is a cavity within which is a point charge q = +2.50×10-6 C.

A) What is the charge on the cavity wall?

B) What is the charge on the outer surface of the conductor?

A) What is the charge on the cavity wall?

B) What is the charge on the outer surface of the conductor?

A) 6.45×10^5 N/C

B) 4.73×10^5 N/C

C) 0 N/C

D) 0 N/C

(3.8)

B) 4.73×10^5 N/C

C) 0 N/C

D) 0 N/C

(3.8)

In the figure a sphere, of radius a = 11.8 cm and charge q = 2.00×10-6 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 27.1 cm and outer radius c = 29.1 cm . This shell has a net charge of -q.

A) Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r < a). Evaluate for r = 5.9 cm. B) Find expressions for the electric field, as a function of the radius r, between the sphere and the shell (a < r < b). Evaluate for r=19.5 cm. C) Find expressions for the electric field, as a function of the radius r, outside the shell (r > c). Evaluate for r = 30.1 cm.

D)What is the charge on the outer surface of the shell?

A) Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r < a). Evaluate for r = 5.9 cm. B) Find expressions for the electric field, as a function of the radius r, between the sphere and the shell (a < r < b). Evaluate for r=19.5 cm. C) Find expressions for the electric field, as a function of the radius r, outside the shell (r > c). Evaluate for r = 30.1 cm.

D)What is the charge on the outer surface of the shell?

A) 7.06×10^7 N/C

B) 7.06×10^7 N/C

(3.9)

B) 7.06×10^7 N/C

(3.9)

Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R = 5.00×10-2 m. The charge density is 5.00×10-2 C/ m3.

A) What is the electric field at r = 2.50×10-2 m?

B) What is the electric field at r = 1.00×10-1 m?

A) What is the electric field at r = 2.50×10-2 m?

B) What is the electric field at r = 1.00×10-1 m?