Physics222: Chapter 21 *PRACTICE

Electric field lines can cross only if both positive and negative charges are involved.

False

Three point charges are placed on the x-axis. A charge of +2.0 μC is placed at the origin, -2.0 μC to the right at x = 50 cm, and +4.0 μC at the 100 cm mark. What are the magnitude and direction of the electrostatic force which acts on the charge at the origin?

Fnet = 72 x 10-3 N Direction of the electrostatic force will be given as :: Towards the right

Can electric field lines intersect in free space?

No

Two large, flat plates are parallel to each other. Plate A , located at y = 1 cm, is along the xz-plane and carries a uniform charge density σA = -1.00 μC/m2. Plate B is located at y = -1 cm and carries a uniform charge density σB = +2.00 μC/m2. What is the electric field at the point of coordinates (x, y, z) = (-0.5 cm, 0 cm, 0 cm)?

(+1.69x10^5 N/C)

An electric dipole is made of two charges of equal magnitudes and opposite signs. The positive charge, q = 1 μC, is located at the point (x, y, z) = (0, 1 cm, 0) while the negative charge is located at the point (x, y, z) = (0, -1 cm, 0). This dipole is placed in the electric field E⃗ E→= (3 × 106 N/C ) ii . How much energy will be released from the dipole when it turns to its stable equilibrium position?

0.06 J

A 5.0-C charge is 10 m from a small test charge. What is the magnitude of the force experienced by a 1.0 nC charge placed at the location of the test charge?

0.45 N

As shown in Fig. 21-16, a point charge of +Q is placed at the center of a square, and a second point charge of -Q is placed at the upper-left corner. It is observed that an electrostatic force of 2.0 N acts on the positive charge at the center. What is the magnitude of the force that acts on the center charge if a third charge of -Q is placed at the lower-left corner?

2.8N

What are the magnitude and direction of the electric field at a distance of 1.50 m from a 50.0-nC charge?

200 N/C away from the charge

A 1.0-C charge is 15 m from a second charge, and the force between them is 1.0 N. What is the magnitude of the second charge?

25 nC

A thin, circular disk of radius R = 30 cm is oriented in the yz-plane with its center as the origin. The disk carries a total charge Q = +3 μC distributed uniformly over its surface. Calculate the magnitude of the electric field due to the disk at the point x = 15 cm along the x-axis.

3.32 × 10^5 N/C

A dipole moment is placed in a uniform electric field oriented along an unknown direction. The maximum torque applied to the dipole is equal to 0.1 N.m. When the dipole reaches equilibrium its potential energy is equal to -0.2 J. What was the initial angle between the direction of the dipole moment and the direction of the electric field?

30°

As shown in Fig. 21-17, a point charge of +Q is placed at the centroid of an equilateral triangle. When a second charge of +Q is placed at one of the triangle's vertices, an electrostatic force of 4.0 N acts on it. What is the magnitude of the force that acts on the center charge due to a third charge of +Q placed at one of the other vertices?

4.0N

Two point charges of magnitudes +5.00 μC, and +7.00 μC are placed along the x-axis at x = 0 cm and x = 100 cm, respectively. Where must a third charge be placed along the x-axis so that it does not experience any net force because of the other two charges?

45.8 cm

A proton is placed in an electric field of intensity 700 N/C. What is the magnitude and direction of the acceleration of this proton due to this field?

6.71 × 1010 m/s2 in the direction of the electric field

An atomic nucleus has a charge of +40e. An electron is 10-9 m from the nucleus. What is the force on the electron?

9.2 nN

Two equal charges of magnitude +1 C are separated by a distance of 1 km. What is the force acting between these two charges?

9000 N

The direction of the electric field halfway between an electron and a proton is

directed toward the electron

A material is a good conductor because it

has numerous free electrons

The electric field shown in Fig. 21-13

increases to the right.

Materials in which the electrons are bound very tightly to the nuclei are referred to as

insulators.

Four point charges of equal magnitudes but with varying signs are arranged on three of the corners and at the center of the square of side d as shown in Fig. 21-2. Which of the arrows shown represents the net force acting on the center charge?

A

Four point charges of varying magnitude and sign are arranged on the corners of the square of side d as shown in Fig. 21-6. Which of the arrows shown represents the net force acting on the point charge with a charge +Q?

A

Two charges Q1 and Q2 of equal magnitudes and opposite signs are positioned as shown in Fig. 21-7. Which of the shown arrows represents correctly the electric field at point P?

A

Equal charges are located at the vertices of a 3-4-5 triangle. The charge experiencing the largest force is located at

the 53° vertex.

A neutral atom always has A neutral atom always has

the same number of protons as electrons

When five equal positive charges are uniformly spaced along the x-axis, the force on the next to last charge on the right is directed

to the right.

The electric field along the axis of a ring-shaped charge of total charge Q distributed uniformly is given by E = Qx/(4π o(x2 + a2)3/2) where a is the radius of the ring and x is the distance from the center of the ring. The electric field at the center of the ring is zero and at great distances from the ring approaches zero. At what position is the electric field a maximum for positive values of x?

x =a2-√a2

Two charges Q1 = -3 μC and Q2 = +3 μC are located on the y-axis at y1 = -5 cm and respectively. A third charge Q3 = +24 μC is added on the y-axis so that the electric field at the origin is equal to zero. What is the position of Q3?

y3 = -10 cm

Q1 = 6.0 nC is at (0.30 m, 0); Q2 = -1.0 nC is at (0, 0.10 m); Q3 = 5.0 nC is at (0, 0). A.) What is the magnitude of the net force on the 5.0 nC charge? B.)What is the directional angle of the net force on the 5.0 nC charge?

A.) 5.6*10^-6N B.)124 Degrees

A conductor is placed in an electric field under electrostatic conditions. Which of the following statements is correct for this situation?

All of the previous answers apply

Four point charges of equal magnitude and varying signs are arranged on corners of the square of side d as shown in Fig. 21-4. Which of the arrows shown represents the net force acting on the charge at the upper right hand corner of the square?

B

Three equal charges are at three of the corners of a square of side d. A fourth charge of equal magnitude is at the center of the square as shown in Fig. 21-1. Which of the arrows shown represents the net force acting on the charge at the center of the square?

B

A 5.0-μC charge is placed at the 0 cm mark of a meter stick and a -4.0 μC charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field zero?

The E field is zero beyond 50, however. It will be zeroat q / r2 = q / r2 5 / x2 = 4 / (x -50)2 5 ( x2 - 100 x + 2500) = 4x2 x2 - 500x + 12500 = 0 x = 474 cm = 4.7 m

Three equal point charges are placed at three of the corners of a square of side d as shown in Fig. 21-9. Which of the arrows shown represents the direction of the net electric field at the center of the square?

C

Two charged objects are separated by a distance d. The first charge is larger in magnitude than the second charge.

The charges exert forces on each other equal in magnitude and opposite in direction.

Two large, flat, horizontally oriented plates are parallel to each other, a distance d apart. Plate A has a uniform, positive charge density of magnitude σA. Plate B has a uniform, negative charge density of magnitude σB . What is the magnitude of the electric field half-way between the two plates?

The net electric field is (1/2eEo)(Oa+Ob)

Four point charges of equal magnitude and sign are arranged on the corners of the square of side d as shown in Fig. 21-5. Which of the arrows shown represents the net force acting on the charge at the upper right hand corner of the square?

D

When static equilibrium is established for a charged conductor, the electric field just inside the surface of the conductor is

Zero

An atom has more electrons than protons. The atom is

a negative ion.

In a region where the electric field is uniform, the electric field lines

are parallel to one another and equally spaced.

An originally neutral electroscope is briefly touched with a positively charged glass rod. The electroscope

becomes positively charged.

A long, thin rod parallel to the y-axis is located at x = - 1 cm and carries a uniform positive charge density λ = 1 nC/m . A second long, thin rod parallel to the z-axis is located at x = +1 cm and carries a uniform negative charge density λ = - 1 nC/m. What is the electric field at the origin?

(3.6 × 10^3 N/C)

A charge Q = 3 μC is located at the origin. The electric field created by this charge at a point of coordinates (x = 2 m, is equal to

(6.75 × 103 N/C)

Fig. 21-14 shows electric field lines near two electric point charges. If Q1 = -1 μC, what is the value of Q2?

+2 μC

Two point charges of magnitude +7.00 μC and -9.00 μC are placed along the x-axis at x = 0 cm and x = 40.0 cm, respectively. Where must a third charge, q, be placed along the x-axis so that it does not experience any net force because of the other two charges?

-2.99 m

If the earth's electric field is 100 N/C downward, what must be the charge on a 1-kg object so that it would be "weightless"?

-9.8 × 10-2 C

Four equal negative point charges are located at the corners of a square, their positions in the x-y plane being (1, 1), (-1, 1), The direction of the electric field on the x-axis at (1, 0) is

-i

Three point charges are located at the following positions: Q1 = 2.00 μC at x = 1.00 m; Q2 = 3.00 C at x = 0; Q3 = -5.00 μC at What is the magnitude of the force on the 3.00-μC charge?

0.189 N

State three properties of conductors in static equilibrium.

1. charges if any reside only on surface. 2. electric field inside conductor is always zero. 3. electric potential at all points of conductor is same.

An electric dipole of dipole moment = (5 × 10-10 C.m) is placed in an electric field = (2 × 106 N/C) +(2 × 106 N/C) . What is the maximum torque experienced by the dipole?

1.00 × 10-3 N.m

Consider a square which is 1.0 m on a side. Charges are placed at the corners of the square as follows: +4.0 μC at (0, 0); +4.0 C at (1, 1); +3.0 μC at (1, 0); -3.0 μC at (0, 1). What is the magnitude of the electric field at the square's center?

1.1 × 105 N/C

A piece of plastic has a net charge of +2.00 μC. How many more protons than electrons does this piece of plastic have?

1.25 × 1013

Two point charges, initially 2.0 cm apart, experience a 1.0-N force. If they are moved to a new separation of 8.0 cm, what is the electric force between them?

1/16 N

A 10 microcoulomb charge is placed at the origin and a 20 microcoulomb charge is placed on the x-axis at x = 40 cm. If an electron is placed on the y-axis at y = 30 cm, what is the magnitude of the force it will experience?

2.46 × 10-13 N

Two point charges of +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What is the intensity of electric field E midway between these two charges?

25.2 × 106 N/C directed towards the negative charge

The force of attraction between a -40.0 μC and +108 μC charge is 4.00 N. What is the separation between these two charges?

3.12 m

A copper penny has a mass of 3.0 g. A total of 4.0 × 1012 electrons are transferred from one neutral penny to another. If the electrostatic force of attraction between the pennies is equal to the weight of a penny, what is the separation between them?

35 cm

An electric field is set up between two parallel plates, each of area 2.0 m2, by putting 1.0 μC charge on one plate and a -1.0 C charge on the other. The plates are separated by 4.0 mm. What is the magnitude of the electric field between the plates at a distance of 1.0 mm from the positive plate?

5.6 × 104 N/C

An atomic nucleus has a charge of +40e. What is the magnitude of the electric field at a distance of 1.0 m from the nucleus?

5.8 × 10-8 N/C

A metal sphere of radius 2.0 cm carries a charge of 3.0 μC. What is the electric field 6.0 cm from the center of the sphere?

7.5 × 106 N/C

A metal sphere of radius 10 cm carries a charge of +2.0 μC. What is the magnitude of the electric field 5.0 cm outside the sphere's surface?

8.0 × 105 N/C

Three equal charges are located in the x-y plane with coordinates (0, 3m), (4m, 3m), and (4m, 0). The direction of the force on the charge located at (4m, 3m) is the same as the direction of

9 + 16.

Fig. 21-12 shows two electric charges of equal magnitudes and opposite signs. Electric field lines surrounding the charges are also shown. Which of the shown arrows correctly represents the electric field vector at point P?

A

Four point charges of equal magnitude but with varying signs are arranged on three of the corners and at the center of the square of side d as shown in Fig. 21-3. Which of the arrows shown represents the net force acting on the center charge?

A

Three equal point charges are placed at the corners of a square of side d as shown in Fig. 21-8. What is the correct expression of the net electric field at the center of the square?

A

Three equal point charges are placed at the corners of a square of side d as shown in Fig. 21-8. Which of the arrows shown represents the direction of the net electric field at the center of the square?

A

Three equal point charges of varying signs are placed on the corners of a square of side d as shown in Fig. 21-15. What is the correct expression for the magnitude of the net electric field at the center of the squar

A

Which of the arrows shown in Fig. 21-10 represents the correct direction of the electric field between the two metal plates?

A

Two large, flat, horizontally oriented plates are parallel to each other, a distance d apart. Half-way between the two plates the electric field field has a 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

Four charges of magnitude +q are placed at the corners of a square whose sides have a length d. What is the magnitude of the total force exerted by the four charges on a charge Q located a distance b along a line perpendicular to the plane of the square and equidistant from the four charges?

Force between two point charges = K*q1*q2 / r^2K is a constant. r represents distance between the charges.K = 9 * 10^9 N m^2/C^2Therefore total Force (ma) = 4 * K * q * q / d ^2 (r = d for this case)

Is it possible to have a zero electric field value between a negative and positive charge along the line joining the two charges?

No, a zero electric field cannot exist between the two charges.

Fig. 21-11 shows 3 electric charges labeled Q1, Q2, Q3 and some electric field lines in the region surrounding the charges. What are the signs of the 3 charges?

Q1 is positive, Q2 is negative, Q3 is positive.

State the law of conservation of electric charge.

The law of conservation of charge states that electric charge can neither be created nor destroyed. In a closed system, the amount of charge remains the same. When something changes its charge it doesn't create charge but transfers it.

Compare insulators and conductors on the atomic level.

The most common difference between the two is that while conductors allow free flow of electrons from one atom to another, insulators restrict free flow of electrons. Conductors allow electrical energy to pass through them, whereas insulators do not allow electrical energy to pass through them

A solid block of metal in electrostatic equilibrium is placed in a uniform electric field. Give a statement concerning the electric field in the block's interior.

There is no electric field in the block's interior.

A positive object touches a neutral electroscope, and the leaves separate. Then a negative object is brought near the electroscope, but does not touch it. What happens to the leaves?

They move closer together.

Three point charges each equal to 10 microcoulombs are located at x = 1m, x = 2m, and x = 3m, respectively, on the x-axis. What is the magnitude of the electric field at the origin?

Three point charges each equal to 10 microcoulombs are located at x = 1m, x = 2m, and x = 3m, respectively, on the x-axis. What is the magnitude of the electric field at the origin?

A positive charge placed in an electric field experiences a force in the direction of the field.

True

If a conductor is placed in an electric field under electrostatic conditions, the electric field is excluded from the inside of the conductor.

True

Two point charges each have a value of 3.0 C and are separated by a distance of 4.0 m. What is the electric field at a point midway between the two charges?

Two point charges each have a value of 3.0 C and are separated by a distance of 4.0 m. What is the electric field at a point midway between the two charges?

Is it possible to have a zero electric field value between two positive charges along the line joining the two charges?

Yes, regardless of the magnitude of the two charges.

If two uncharged objects are rubbed together and one of them acquires a positive charge then the other one

acquires a negative charge.

When atom A loses an electron to atom B,

atom A becomes a positive ion and atom B becomes a negative ion

Materials in which the electrons are bound very loosely to the nuclei and can move about freely within the material are referred to as

conductors.

An originally neutral electroscope is grounded briefly while a positively charged glass rod is held near it. After the glass rod is removed, the electroscope

is negatively charged.

If an electroscope is charged by induction

its leaves will separate because of the interaction of the charges.

A ring of negative, uniform charge density is placed on the xz-plane with the center of the ring at the origin. A positive charge moves along the y axis toward the center of the ring. At the moment the charge passes through the center of the ring

its velocity is maximum and its acceleration is zero. (The positive charge will acceleratetowards the center of the ring and the magnitude of the acceleration willdecrease to zero as it reaches the center of the ring. So as the charge passesthru the center, its acceleration will be zero and the velocity will be constant.)

If an atom has become a positive ion, it has

lost an electron or electrons.

A negatively charged rod is brought near one end of an uncharged metal bar. The end of the metal bar farthest from the charged rod will be charged

negative.

In deriving the axial electric field for the ring-shaped charge distribution and the electric field from a long line of charge, the component perpendicular to the resulting field is zero because of what physical property?

symmetry

The number of protons in the nucleus of an electrically neutral atom is equal to

the number of electrons surrounding the nucleus

A long line of charge with uniform linear charge density λ1λ1 is located on the xx-axis and another long line of charge with uniform linear charge density λ2λ2 is located on the yy-axis with their centers crossing at the origin. In what direction is the electric field at point zz = aa on the positive zz-axis if λ1λ1 and λ2λ2 are positive?

the positive z-direction

An electron and a proton, are released simultaneously from rest and start to move towards each other because of the attractive Coulomb force between them. They are initially separated by a distance d. The two particles eventually collide. When they collide,

they are closer to the proton's initial position. (The proton is going to be a lot less likely to move because it has a much greater mass than the electron.)

A charge Q1 is located at coordinates (x = +a, y = +a). A second charge Q2 , identical to Q1, is located in such a way that the net electric field at the origin of the coordinate axis (x = 0, y = 0) is equal to 0. What are the coordinates of Q2?

x = -a, y = -a

A charge +3q is placed at x = 0 and a charge +11q is placed at x = 5 units. Where, along the x-axis is the net force on a charge Q equal to zero?

x = 1.72 units