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One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure.The balls are in equilibrium a distance d apart.If the charge on each ball is doubled,the distance between the balls in the test tube would become One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure.The balls are in equilibrium a distance d apart.If the charge on each ball is doubled,the distance between the balls in the test tube would become A) d. B) 2d. C) 4d. D) 8d.


A) One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure.The balls are in equilibrium a distance d apart.If the charge on each ball is doubled,the distance between the balls in the test tube would become A) d. B) 2d. C) 4d. D) 8d. d.
B) 2d.
C) 4d.
D) 8d.

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In the figure,a ring 0.71 m in radius carries a charge of + 580 nC uniformly distributed over it.A point charge Q is placed at the center of the ring.The electric field is equal to zero at field point P,which is on the axis of the ring,and 0.73 m from its center. In the figure,a ring 0.71 m in radius carries a charge of + 580 nC uniformly distributed over it.A point charge Q is placed at the center of the ring.The electric field is equal to zero at field point P,which is on the axis of the ring,and 0.73 m from its center. The point charge Q is closest to A) -210. B) -300. C) -420. D) 210. E) 300. The point charge Q is closest to In the figure,a ring 0.71 m in radius carries a charge of + 580 nC uniformly distributed over it.A point charge Q is placed at the center of the ring.The electric field is equal to zero at field point P,which is on the axis of the ring,and 0.73 m from its center. The point charge Q is closest to A) -210. B) -300. C) -420. D) 210. E) 300.


A) -210.
B) -300.
C) -420.
D) 210.
E) 300.

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Two thin 80.0-cm rods are oriented at right angles to each other.Each rod has one end at the origin of the coordinates,and one of them extends along the +x-axis while the other extends along the +y-axis.The rod along the +x-axis carries a charge of -15.0 µC distributed uniformly along its length,and the other rod carries +15.0 µC uniformly over its length.Find the magnitude and direction of the net electrical force that these two rods exert on an electron located at the point (40.0 cm,40.0 cm). Two thin 80.0-cm rods are oriented at right angles to each other.Each rod has one end at the origin of the coordinates,and one of them extends along the +x-axis while the other extends along the +y-axis.The rod along the +x-axis carries a charge of -15.0 µC distributed uniformly along its length,and the other rod carries +15.0 µC uniformly over its length.Find the magnitude and direction of the net electrical force that these two rods exert on an electron located at the point (40.0 cm,40.0 cm). , , Two thin 80.0-cm rods are oriented at right angles to each other.Each rod has one end at the origin of the coordinates,and one of them extends along the +x-axis while the other extends along the +y-axis.The rod along the +x-axis carries a charge of -15.0 µC distributed uniformly along its length,and the other rod carries +15.0 µC uniformly over its length.Find the magnitude and direction of the net electrical force that these two rods exert on an electron located at the point (40.0 cm,40.0 cm). ,

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1.35 × 10-13 ...

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A small glass bead has been charged to 8.0 nC.What is the magnitude of the electric field A small glass bead has been charged to 8.0 nC.What is the magnitude of the electric field from the center of the bead? (k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N • m<sup>2</sup>/C<sup>2</sup>) A) 1.8 × 10<sup>5</sup> N/C B) 3.6 × 10<sup>3</sup> N/C C) 1.4 × 10<sup>-3</sup> N/C D) 3.6 × 10<sup>-6</sup> N/C from the center of the bead? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)


A) 1.8 × 105 N/C
B) 3.6 × 103 N/C
C) 1.4 × 10-3 N/C
D) 3.6 × 10-6 N/C

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In the figure,a proton is projected horizontally midway between two parallel plates that are separated by In the figure,a proton is projected horizontally midway between two parallel plates that are separated by The electrical field due to the plates has magnitude between the plates away from the edges.If the plates are long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. , , The electrical field due to the plates has magnitude In the figure,a proton is projected horizontally midway between two parallel plates that are separated by The electrical field due to the plates has magnitude between the plates away from the edges.If the plates are long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. , , between the plates away from the edges.If the plates are In the figure,a proton is projected horizontally midway between two parallel plates that are separated by The electrical field due to the plates has magnitude between the plates away from the edges.If the plates are long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. , , long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. In the figure,a proton is projected horizontally midway between two parallel plates that are separated by The electrical field due to the plates has magnitude between the plates away from the edges.If the plates are long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. , , , In the figure,a proton is projected horizontally midway between two parallel plates that are separated by The electrical field due to the plates has magnitude between the plates away from the edges.If the plates are long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. , , , In the figure,a proton is projected horizontally midway between two parallel plates that are separated by The electrical field due to the plates has magnitude between the plates away from the edges.If the plates are long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. , , In the figure,a proton is projected horizontally midway between two parallel plates that are separated by The electrical field due to the plates has magnitude between the plates away from the edges.If the plates are long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. , ,

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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 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) . Sphere Y is now moved away from X,as in Figure (b) . What are the final charge states of X and Y? A) Both X and Y are neutral. B) X is positive and Y is neutral. C) X is neutral and Y is positive. D) X is negative and Y is positive. E) Both X and Y are negative. Sphere Y is now moved away from X,as in Figure (b) . 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) . Sphere Y is now moved away from X,as in Figure (b) . What are the final charge states of X and Y? A) Both X and Y are neutral. B) X is positive and Y is neutral. C) X is neutral and Y is positive. D) X is negative and Y is positive. E) Both X and Y are negative. What are the final charge states of X and Y?


A) Both X and Y are neutral.
B) X is positive and Y is neutral.
C) X is neutral and Y is positive.
D) X is negative and Y is positive.
E) Both X and Y are negative.

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In the figure,all the charges are point charges and the charge in the middle is In the figure,all the charges are point charges and the charge in the middle is For what charge q<sub>1</sub> will charge q<sub>2</sub> be in static equilibrium? A) 12 nC B) 6.2 nC C) 3.1 nC D) 25 nC For what charge q1 will charge q2 be in static equilibrium? In the figure,all the charges are point charges and the charge in the middle is For what charge q<sub>1</sub> will charge q<sub>2</sub> be in static equilibrium? A) 12 nC B) 6.2 nC C) 3.1 nC D) 25 nC


A) 12 nC
B) 6.2 nC
C) 3.1 nC
D) 25 nC

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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 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 along the x-axis. A) 9.95 × 10<sup>5</sup> N/C B) 4.98 × 10<sup>5</sup> N/C C) 3.31 × 10<sup>5</sup> N/C D) 2.49 × 10<sup>5</sup> N/C E) 1.99 × 10<sup>5</sup> N/C along the x-axis. 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 along the x-axis. A) 9.95 × 10<sup>5</sup> N/C B) 4.98 × 10<sup>5</sup> N/C C) 3.31 × 10<sup>5</sup> N/C D) 2.49 × 10<sup>5</sup> N/C E) 1.99 × 10<sup>5</sup> N/C


A) 9.95 × 105 N/C
B) 4.98 × 105 N/C
C) 3.31 × 105 N/C
D) 2.49 × 105 N/C
E) 1.99 × 105 N/C

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Three equal negative point charges are placed at three of the corners of a square of side d.What is the magnitude of the net electric field at the center of the square? Three equal negative point charges are placed at three of the corners of a square of side d.What is the magnitude of the net electric field at the center of the square?

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The electric field strength in the space between two closely spaced parallel disks is The electric field strength in the space between two closely spaced parallel disks is .This field is the result of transferring 3.9 × 10<sup>9</sup> electrons from one disk to the other.What is the diameter of the disks? (e<sub> </sub>= 1.60 × 10<sup>-19 </sup>C, A) 3.0 cm B) 1.5 cm C) 4.5 cm D) 6.0 cm .This field is the result of transferring 3.9 × 109 electrons from one disk to the other.What is the diameter of the disks? (e = 1.60 × 10-19 C, The electric field strength in the space between two closely spaced parallel disks is .This field is the result of transferring 3.9 × 10<sup>9</sup> electrons from one disk to the other.What is the diameter of the disks? (e<sub> </sub>= 1.60 × 10<sup>-19 </sup>C, A) 3.0 cm B) 1.5 cm C) 4.5 cm D) 6.0 cm


A) 3.0 cm
B) 1.5 cm
C) 4.5 cm
D) 6.0 cm

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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


A) zero.
B) 3.6 N, attractive.
C) 5.4 N, attractive.
D) 3.6 N, repulsive.
E) 5.4 N, repulsive.

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A piece of plastic has a net charge of +2.00 μC.How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10-19 C)


A) 1.25 × 1013
B) 1.25 × 1019
C) 2.50 × 1013
D) 2.50 × 1019

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Two small insulating spheres are attached to silk threads and aligned vertically as shown in the figure.These spheres have equal masses of 40 g,and carry charges q1 and q2 of equal magnitude 2.0 μC but opposite sign. The spheres are brought into the positions shown in the figure,with a vertical separation of 15 cm between them.Note that you cannot neglect gravity.(k = 1/4πε0 = Two small insulating spheres are attached to silk threads and aligned vertically as shown in the figure.These spheres have equal masses of 40 g,and carry charges q<sub>1</sub> and q<sub>2</sub> of equal magnitude 2.0 μC but opposite sign.<sup> </sup>The spheres are brought into the positions shown in the figure,with a vertical separation of 15 cm between them.Note that you cannot neglect gravity.(k = 1/4πε<sub>0</sub> = The tension in the lower thread is closest to A) 1.2 N. B) 1.4 N. C) 1.6 N. D) 1.8 N. E) 2.0 N. The tension in the lower thread is closest to Two small insulating spheres are attached to silk threads and aligned vertically as shown in the figure.These spheres have equal masses of 40 g,and carry charges q<sub>1</sub> and q<sub>2</sub> of equal magnitude 2.0 μC but opposite sign.<sup> </sup>The spheres are brought into the positions shown in the figure,with a vertical separation of 15 cm between them.Note that you cannot neglect gravity.(k = 1/4πε<sub>0</sub> = The tension in the lower thread is closest to A) 1.2 N. B) 1.4 N. C) 1.6 N. D) 1.8 N. E) 2.0 N.


A) 1.2 N.
B) 1.4 N.
C) 1.6 N.
D) 1.8 N.
E) 2.0 N.

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A 1.0-C point charge is 15 m from a second point charge,and the electric force on one of them due to the other is 1.0 N.What is the magnitude of the second charge? A 1.0-C point charge is 15 m from a second point charge,and the electric force on one of them due to the other is 1.0 N.What is the magnitude of the second charge? A) 25 C B) 1.0 C C) 10 nC D) 0.025 C E) 25 nC


A) 25 C
B) 1.0 C
C) 10 nC
D) 0.025 C
E) 25 nC

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Three +3.0-μC point charges are at the three corners of a square of side 0.50 m.The last corner is occupied by a -3.0-μC charge.Find the magnitude of the electric field at the center of the square. Three +3.0-μC point charges are at the three corners of a square of side 0.50 m.The last corner is occupied by a -3.0-μC charge.Find the magnitude of the electric field at the center of the square.

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An electric dipole is made of two charges of equal magnitudes and opposite signs.The positive charge,q = 1.0 μC,is located at the point (x,y,z) = (0.00 cm,1.0 cm,0.00 cm) ,while the negative charge is located at the point (x,y,z) = (0.00 cm,-1.0 cm,0.00 cm) .How much work will be done by an electric field An electric dipole is made of two charges of equal magnitudes and opposite signs.The positive charge,q = 1.0 μC,is located at the point (x,y,z) = (0.00 cm,1.0 cm,0.00 cm) ,while the negative charge is located at the point (x,y,z) = (0.00 cm,-1.0 cm,0.00 cm) .How much work will be done by an electric field = (3.0 × 10<sup>6</sup> N/C) to bring the dipole to its stable equilibrium position? A) 0.060 J B) 0.030 J C) 0.00 J D) 0.020 J E) 0.12 J = (3.0 × 106 N/C) An electric dipole is made of two charges of equal magnitudes and opposite signs.The positive charge,q = 1.0 μC,is located at the point (x,y,z) = (0.00 cm,1.0 cm,0.00 cm) ,while the negative charge is located at the point (x,y,z) = (0.00 cm,-1.0 cm,0.00 cm) .How much work will be done by an electric field = (3.0 × 10<sup>6</sup> N/C) to bring the dipole to its stable equilibrium position? A) 0.060 J B) 0.030 J C) 0.00 J D) 0.020 J E) 0.12 J to bring the dipole to its stable equilibrium position?


A) 0.060 J
B) 0.030 J
C) 0.00 J
D) 0.020 J
E) 0.12 J

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The figure shows two unequal point charges,q and Q,of opposite sign.Charge Q has greater magnitude than charge q.In which of the regions X,Y,Z will there be a point at which the net electric field due to these two charges is zero? The figure shows two unequal point charges,q and Q,of opposite sign.Charge Q has greater magnitude than charge q.In which of the regions X,Y,Z will there be a point at which the net electric field due to these two charges is zero? A) only regions X and Z B) only region X C) only region Y D) only region Z E) all three regions


A) only regions X and Z
B) only region X
C) only region Y
D) only region Z
E) all three regions

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


A) Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1) ,(-1,1) ,(-1,-1) ,(1,-1) .The electric field on the x-axis at (1,0) points in the same direction as A) . B) . C) - . D) . E) - . .
B) Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1) ,(-1,1) ,(-1,-1) ,(1,-1) .The electric field on the x-axis at (1,0) points in the same direction as A) . B) . C) - . D) . E) - . .
C) - Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1) ,(-1,1) ,(-1,-1) ,(1,-1) .The electric field on the x-axis at (1,0) points in the same direction as A) . B) . C) - . D) . E) - . .
D) Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1) ,(-1,1) ,(-1,-1) ,(1,-1) .The electric field on the x-axis at (1,0) points in the same direction as A) . B) . C) - . D) . E) - . .
E) - Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1) ,(-1,1) ,(-1,-1) ,(1,-1) .The electric field on the x-axis at (1,0) points in the same direction as A) . B) . C) - . D) . E) - . .

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A 5.0-μC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-μC point charge is placed at the 50 cm mark.At what point on a line joining the two charges is the electric field due to these charges equal to zero?

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4.7 m from...

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A dipole with a positive charge of A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C and a negative charge of A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C


A) 0.56 A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C N/C
B) -0.56 A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C N/C
C) 0.28 A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C N/C
D) -0.28 A dipole with a positive charge of and a negative charge of is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point A) 0.56 N/C B) -0.56 N/C C) 0.28 N/C D) -0.28 N/C N/C

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