PHY 222 Test 1

Two +6.0-μC point charges are placed at the corners of the base of an equilateral triangle, as shown in the figure. (k = 1/4πε0 = 8.99 × 109 N • m2/C2) At the vertex, P, of the triangle (a) what is the electric potential (relative to infinity) due to these charges?(b) what is the magnitude of the electric field due to these charges?

(a) 54 kV (b) 2.3 × 10^4 N/C

The figure shows four Gaussian surfaces surrounding a distribution of charges. (a) Which Gaussian surfaces have an electric flux of +q/ε0 through them?(b) Which Gaussian surfaces have no electric flux through them?

(a) b (b) c

The cross section of a long coaxial cable is shown in the figure, with radii as given. The linear charge density on the inner conductor is and the linear charge density on the outer conductor is −70 𝑛𝐶/𝑚 The inner and outer cylindrical surfaces are respectively denoted by A, B, C, and D, as shown. 𝜖0 = 8.85 × 10−12𝐶2/𝑁𝑚2. What is the radial component of the electric field at a point that 34 mm from the axis?

-1.59x10^4 N/C

The cross section of a long coaxial cable is shown in the figure, with radii as given. The linear charge density on the inner conductor is -30nC/m and the linear charge density on the outer conductor is -70 nC/m. The inner and outer cylindrical surfaces are respectively denoted by A, B, C, and D, as shown. The radial component of the electric field at a point that 34 mm from the axis is closest to

-16,000 N/C

Two extremely large nonconducting horizontal sheets each carry uniform charge density on the surfaces facing each other. The upper sheet carries +5.00 µC/m^2 . The electric field midway between the sheets is 4.25x10^5 N/C pointing downward. What is the surface charge density on the lower sheet?

-2.52 µC/m^2

If the potential in a region is given by V(x,y,z) = xy - 3z-2, then the y component of the electric field in that region is

-x

A charge of 1.0 × 10^-6 μC is located inside a sphere, 1.25 cm from its center. What is the electric flux through the sphere due to this charge?

0.11 N • m^2/C

In the figure, charge 𝑞1= 3.1 × C is placed at the origin and charge 𝑞2 = −8.7 × 10−6 C is placed on the x-axis, at x = -0.20 m. Where along the x-axis can a third charge Q = -8.3 μC be placed such that the resultant force on this third charge is zero?

0.29m

A small sphere with a mass of 441 g is moving upward along the vertical +y-axis when it encounters an electric field of 5.00 N/C i . If, due to this field, the sphere suddenly acquires a horizontal acceleration of 13.0 m/s2 i , what is the charge that it carries?

1.15 C

An extremely long thin wire carries a uniform linear charge density of 358 nC/m. Find the potential difference between points 5.0 m and 6.0 m from the wire, provided they are not near either end of the wire.

1.2 kV

An irregular conductor carries a surface charge density of -6.75 µC/m2 at and in the vicinity of a point P on the surface. An electron is released just above P outside the conductor. What are the magnitude and direction of its acceleration the instant after it is released?

1.34 × 10^17 m/s^2, away from P

A pair of charged conducting plates produces a uniform field of 12,000 N/C, directed to the right, between the plates. The separation of the plates is 40 mm. An electron is projected from plate A, directly toward plate B, with an initial velocity of vo = 2.0 × 107 m/s, as shown in the figure. (e = 1.60 × 10-19 C, ε0 = 8.85 × 10-12 C2/N ∙ m2, mel = 9.11 × 10-31 kg) What is the velocity of the electron as it strikes plate B ?

1.52 x 10^7 m/s

In the figure Q = 5.8 nC and all other quantities are accurate to 2 significant figures. What is the magnitude of the force on the charge Q? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

1.8 x 10^-3 N

Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually leaks off of both spheres. When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be

1/4 F

In the figure, all the charges are point charges and the charge in the middle is Q= -3.1 nC. For what charge q1 will charge q2 be in static equilibrium?

12 nC

A pair of charged conducting plates produces a uniform field of 12,000 N/C, directed to the right, between the plates. The separation of the plates is 40 mm. An electron is projected from plate A, directly toward plate B, with an initial velocity of v0= 1.0 x 10^7 m/s, as shown in the figure. , , The distance of closest approach of the electron to plate B is nearest to

16mm

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field E = (100 N/C) . Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin. (ε0 = 8.85 × 10-12 C2/N • m2)

2.26 × 10^5 N • m^2/C

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform ⃗ electric field 𝐸 = (100 N/C) 𝑖̂ . Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin. (ε0 = 8.85 × 10-12 C2/N ∙ m2)

2.26x10^5 Nm^2/C

Two point charges of +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What is the magnitude of electric field due to these charges at a point midway between them?

25.2 × 10^6 N/C directed toward the negative charge

The electric field strength in the space between two closely spaced parallel disks is 1.0x10^5 N/C. This field is the result of transferring 3.9 × 10^9 electrons from one disk to the other. What is the diameter of the disks? (e = 1.60 × 10-19 C,

3.0 cm

A thin, circular disk of radius 30.0 cm is oriented in the yz-plane with its center at the origin. The disk carries a total charge of +3.00 μC distributed uniformly over its surface. Calculate the magnitude of the electric field due to the disk at the point x = 15.0 cm along the x-axis. (ε0 = 8.85 × 10-12 C2/N ∙ m2)

3.31 x 10^5 N/C

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere, does the electric field reach a value equal to half its maximum value?

3.5 cm and 9.9 cm

Two identical small conducting spheres are separated by 0.60 m. The spheres carry different amounts of charge and each sphere experiences an attractive electric force of 10.8N. The total charge on the two spheres is -24 μC. The two spheres are now connected by a slender conducting wire, which is then removed. The electric force on each sphere is closest to

3.6 N, repulsive

Two flat 4.0 cm × 4.0 cm electrodes carrying equal but opposite charges are spaced 2.0 mm apart with their midpoints opposite each other. Between the electrodes but not near their edges, the electric field strength is 2.5 × 10^6 N/C. What is the magnitude of the charge on each electrode?

35 nC

A conducting sphere 45 cm in diameter carries an excess of charge, and no other charges are present. You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) The excess charge on this sphere is closest to

350 nC.

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries an excess charge of -500 nC . A point charge of +300 nC is present at the center. The surface charge density on the inner spherical surface is closest to

4.0 × 10^-8 C/ m^2

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. What is the maximum magnitude of the electric field due to this sphere?

4.17x10^4 N/C

Electric charge is uniformly distributed inside a nonconducting sphere of radius . The electric field at a point P, which is 0.50 m from the center of the sphere, is and is directed radially outward. What is the maximum magnitude of the electric field due to this sphere?

42,000 N/C

Charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = -1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0). What are the magnitude and direction of the net electrostatic force on the 5.0-nC charge due to the other charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

5.4x10^-6 N ; 56 degrees above the -x axis

If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed?

5.9 × 10^7 m/s

A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity?

50V

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC, and no other charges are present. (k = 1/4πε0 = The potential (relative to infinity) due to this sphere at a point 12.0 cm from its center is closest to

674 kV

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC, and no other charges are present. The potential (relative to infinity) due to this sphere at a point 12.0 cm from its center is closest to

674 kV

A very long wire carries a uniform linear charge density of 7.0 nC/m What is the electric field strength 16.0m from the center of the wire at a point on the wire's perpendicular bisector?

7.9 N/C

A metal sphere of radius 10 cm carries a charge of +2.0 μC uniformly distributed over its surface. What is the magnitude of the electric field due to this sphere at a point 5.0 cm outside the sphere's surface?

8.0 × 10^5 N/C

A -7.0-μC point charge has a positively charged object in an elliptical orbit around it. If the mass of the positively charged object is 1.0 kg and the distance varies from 5.0 mm to 20.0 mm between the charges, what is the maximum electric potential difference through which the positive object moves?

9.4 MV

Two concentric conducting spherical shells produce a radially outward electric field of magnitude 49,000 N/C at a point 4.10 m from the center of the shells. The outer surface of the larger shell has a radius of 3.75 m. If the inner shell contains an excess charge of -5.30 μC, find the amount of charge on the outer surface of the larger shell.

91.6 µC

A positive point charge Q is fixed on a very large horizontal frictionless tabletop. A second positive point charge q is released from rest near the stationary charge and is free to move. Which statement best describes the motion of q after it is released?

As it moves farther and farther from Q, its speed will keep increasing

Three equal negative point charges are placed at three of the corners of a square of side d as shown in the figure. Which of the arrows represents the direction of the net electric field at the center of the square?

C

At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?

D/2

Two large, flat, horizontally oriented plates are parallel to each other, a distance d apart. Half way between the two plates the electric field has magnitude E. If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

E

A charge Q is uniformly spread over one surface of a very large nonconducting square elastic sheet having sides of length d. At a point P that is 1.25 cm outside the sheet, the magnitude of the electric field due to the sheet is E. If the sheet is now stretched so that its sides have length 2d, what is the magnitude of the electric field at P?

E/4

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume. At a radial distance r1 = R/4 from the center, the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 2R?

E0

A point charge Q is located a short distance from a point charge 3Q, and no other charges are present. If the electrical force on Q is F, what is the electrical force on 3Q?

F

Two very large parallel sheets a distance d apart have their centers directly opposite each other. The sheets carry equal but opposite uniform surface charge densities. A point charge that is placed near the middle of the sheets a distance d/2 from each of them feels an electrical force F due to the sheets. If this charge is now moved closer to one of the sheets so that it is a distance d/4 from that sheet, what force will feel?

F

If the electric field is zero everywhere inside a region of space, the potential must also be zero in that region.

False

If the electric flux through a closed surface is zero, the electric field at points on that surface must be zero.

False

Two equal positive charges are held in place at a fixed distance. If you put a third positive charge midway between these two charges, its electrical potential energy of the system (relative to infinity) is zero because the electrical forces on the third charge due to the two fixed charges just balance each other.

False

When the electric field is zero at a point, the potential must also be zero there.

False

Which statements are true for an electron moving in the direction of an electric field? (There may be more than one correct choice.)

Its potential energy increases as its kinetic energy decreases. Its kinetic energy decreases as it moves in the direction of the electric field. Its electric potential energy increases as it goes from high to low potential.

A negative charge is moved from point A to point B along an equipotential surface. Which of the following statements must be true for this case?

No work is required to move the negative charge from point A to point B.

The figure shows three electric charges labeled Q1, Q2, Q3, and some electric field lines in the region surrounding the charges. What are the signs of the three charges?

Q1 is positive, Q2 is negative, Q3 is positive

Consider a spherical Gaussian surface of radius R centered at the origin. A charge Q is placed inside the sphere. To maximize the magnitude of the flux of the electric field through the Gaussian surface, the charge should be located

The charge can be located anywhere, since flux does not depend on the position of the charge as long as it is inside the sphere.

Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.)

The electric flux passing through a Gaussian surface depends only on the amount of charge inside that surface, not on its size or shape. If a Gaussian surface is completely inside an electrostatic conductor, the electric field must always be zero at all points on that surface.

Suppose a region of space has a uniform electric field, directed towards the right, as shown in the figure. Which statement about the electric potential is true?

The potential at points A and B are equal, and the potential at point C is lower than the potential at point A.

A conducting sphere contains positive charge distributed uniformly over its surface. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)

The potential at the center of the sphere is the same as the potential at the surface.

A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)

The potential is highest at the center of the sphere.

X and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A positively charged rod R is brought close to X as shown in Figure (a).

X is negative and Y is positive

The graph in the figure shows the electric field strength (not the field lines) as a function of distance from the center for a pair of concentric uniformly charged spheres. Which of the following situations could the graph plausibly represent? (There may be more than one correct choice.)

a positively charged nonconducting thin-walled spherical shell inside of a positively charged conducting sphere a positively charged conducting sphere within another positively charged conducting sphere

Two +6.0-μC point charges are placed at the corners of the base of an equilateral triangle, as shown in the figure. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) At the vertex, P, of the triangle (a) what is the electric potential (relative to infinity) due to these charges? (b) what is the magnitude of the electric field due to these charges?

a) 13,500 N/C b) 2.3x10^4 N/C

Two positive point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) a) What is the potential at point A (relative to infinity) due to these charges? (b) What is the potential at point B (relative to infinity) due to these charges?

a) kq1/r1A + kq2/r2A b) kq1/r1B + kq2/r2B

Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great as the charge density on line #1. The locus of points where the electric field due to these lines is zero is

along a line between the lines closer to line #1 than line #2

When two point charges are a distance d part, the electric force that each one feels from the other has magnitude F. In order to make this force twice as strong, the distance would have to be changed to

d/sqrt(2)

A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere?

graph(horizontal line then half concave up)

Suppose you have two point charges of opposite sign. As you move them farther and farther apart, the potential energy of this system relative to infinity

increases

Under electrostatic conditions, the electric field just outside the surface of any charged conductor

is always perpendicular to the surface of the conductor.

A half-ring (semicircle) of uniformly distributed charge Q has radius R. What is the electric potential at its center?

kQ/r

An electron is initially moving to the right when it enters a uniform electric field directed upwards. Which trajectory shown below will the electron follow?

trajectory Z

Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively. Where should a third charge of +3.0-μC be placed on the +x-axis so that the potential at the origin is equal to zero? =

x = 3.0 cm